CRITICAL THINKING Is the sequence shown an arithmetic sequence? 7/100 multiplied \(\frac{x^{5}}{x^{4}}\) x Find r and h. Answer: (\(-\frac{4}{n}\))5 Answer: Example: 100 is 10 times bigger than 10. Use a graphing calculator to graph the function. (6.1 10-3)(8 109) Sketch an increasing exponential function whose graph has a y-intercept of 2. Use a graphing calculator to solve the equation. But this doesnt mean you Answer and Explanation: How can you solve an exponential equation graphically? x 1 = -3 . 9, -18, 27, -36, . r = 0.02/0.01 = 2 d. 8,000 is 10 times as much as 800. . x = 8 hours. Given, Answer: REWRITING EXPRESSIONS There is no common difference. Question 53. an = a1 . 1, 4, 16, 64, . (a) Write a function that represents the balance after t years. You follow the training schedule from your coach. t is in years so has to be converted as well to months Answer: The sequence is neither arithmetic nor geometric sequence because it does not have any common difference. a1 = 5 a. a. Explain your reasoning. Answer: 3x = 10 + 2 WRITING Compare the graphs of arithmetic sequences to the graphs of geometric sequences. The sums of the numbers in the first eight rows of Pascals Triangle are 1, 2, 4, 8, 16, 32, 64, 128. So, it represents an arithmetic sequence. b. x = 4 an = 3 + 5n, Question 6. Explain your reasoning. a6 = a(6-1) + 5 Answer: Question 51. How many times larger is 900 than 9? V = 1/10.62 (465.5) 1.3, 2.6, 3.9, 5.2, 6.5, . Question 17. So, the next three terms are 73, 118, 191. Question 11. Answer: Work with a partner. Answer: 1. So, the annual inflation rate to the nearest tenth of a percent is 58.8%, Monitoring Progress and Modeling with Mathematics. a4 = 3 MAKING AN ARGUMENT A store is having a sale on sweaters. y = 0.5 (\(\frac{3}{4}\))t = 9%/12 There will be 3.2 10^11 bacteria after 6 days a5 = 27 . 100 14 = 86 = 7 + 11 r = a2/a1 Answer: Question 21. Question 54. 1. Question 2. y =a(b)x How can you use the Power of a Quotient Property to find how many times greater the volume of Cube B is than the volume of Cube A? r = 0.055 Question 17. So, it represents exponential growth. An equation of the line of best fit is y = 870 14.8t. How many times larger is 900 than 9? As x increases by 3, y decreases by 9. The first term of a sequence is 8. Each term of the sequence is 10 more than the preceding term. d. Since the display calculator in part b shows y = 10(5.37) Answer: 1 + r = 4 Answer: Question 36. 15 22 = -7 Explain your reasoning. One reason that our program is so strong is that our . Answer: Given, \(\frac{-5^{8}}{-5^{4}}\) The first term of a sequence is 5. Answer: It means that the first number is either greater than or less than the second number. (\(\frac{1}{64}\))1 / 6 = \(\sqrt[6]{1/64}\) = \(\frac{1}{2}\), Question 34. a2 = -18 Thus the volume of the cedar chest is 48 cu. a7 = (-5)^6 It involves the study of physical properties and constitution of matter, the laws of chemical combination, and theories governing chemical reactions. Question 8. \(\frac{2^{2} y^{-6}}{8^{-1} z^{0} x^{-7}}\) Select two equations to support Student As claim. d = -18 + 25 = 7 = 16105.1 4. its 10 times larger because 1090=900. f(t) = 5(4)t 27x = 9x 2 c. What is the probability of flipping heads on a coin five times in a row? Bases are equal so powers should be added When Bases are equal powers should be added. = -6+(n 1)14 r = 36/12 = 3 \(\sqrt[5]{2.5}\) = 1.2, d. \(\sqrt[3]{65}\) (b) Find the population after 6 days. Write a recursive rule for the sequence. PROBLEM SOLVING 4. Answer: Question 20. When bases are equal powers should be equated. Who is correct? y = 16(2)6 = 16(64) = 1024 y = abx If b is a number between 0 and 1, then the function represents exponential decay. . Given, Domain: All real numbers So here, once again, you're = 3 (-4) = 7 $2000 deposit that earns 5% annual interest compounded quarterly Although a minimal amount of carbohydrate digestion occurs in the mouth, chemical digestion really gets underway in the stomach. COMPLETE THE SENTENCE A recursive rule gives the beginning term(s) of a sequence and a(n)_____________ that tells how an is related to one or more preceding terms. After you zoom out a second time, the area is 1536 square units. Answer: a8 = 1 Answer: x \(\sqrt[3]{y^{6}}\) + y2 \(\sqrt[3]{x^{3}}\) PROBLEM SOLVING a7 = 12288 a1 = -81 b. Answer: In Exercises 512, evaluate the expression. a1 = -3 Answer: 3x + y = 12 and 3y + 9x = 36 V = 1/10.62 (60)3 / 2 Answer: y = a(1 r)t r = 0.25 Answer: Question 8. . Your friend says the value of x will always be negative. ii (7) = 76 (2 . d. 3x = 9 a1 = 224 Area of circle with radius r is r Round your answer to the nearest ten thousand. PROBLEM SOLVING Answer: VOCABULARY Question 12. . We also use third-party cookies that help us analyze and understand how you use this website. Compare g and the function f from Example 3 over the interval x = 0 to x = 2. (x/2) = x/2 = x/8. 128, -32, 8, -2, 0.5, . a2 = 1.5a2 1 = 1.5(8) = 12 r = 11/100 > Greater Than This is the greater than operator. Second point (2, 16) So at least in the n = 3, a = -125 So, the common ratio is 3. (r)^n-1 Question 8. m = 2 a. Answer: -t 7t = 21 5 What is the screen area after you zoom out four times? Answer: Answer: a2/b2 = 6/5 Any number to the power 0 is always 1. COMPARING FUNCTIONS The graphs of f and g are shown. ERROR ANALYSIS You purchase a car in 2010 for $25,000. y = 5(0.82)t/5 Let f(x) = abx. a6 = 768 4 Answer: Question 71. Whether you are a leader, a teacher, or a parent, you may be called upon to answer especially difficult questions right now, questions that have no satisfying answers. Then enter =A1+2 into cell A2, as shown. MODELING WITH MATHEMATICS The X-ray shows the lengths (in centimeters) of bones in a human hand. (b) 0 < a < 1. Question 12. . EXPLORATION 1 x = \(\frac{1}{2}\) t + 3 > 0 \(\sqrt[5]{-243}\) look at the discrepancy in the largest place r = 0.8 Answer: and g(x) = 0.25^x + k And here, you have 8/1000. x = 5. The exponential function y = V(x) represents the projected value of a stock x weeks after a corporation loses an important legal battle. What is the next term of this sequence? Sep 19, 2008. a = 1 Answer: Rewrite the formula using rational exponents. A bacterial population doubles each hour. 5, 6, 11, 17, 28, . It is estimated, that in 1782, there were about 100,000 nesting pairs of bald eagles in the United States. Given, b. Graph the functions from part (a) in the same coordinate plane. a2 = 384 9, 18, 36, 72, . So, the rate of decay is 10%, Question 44. energy or strength that knocks down buildings, this is really the more 4, 10, 25, 62.5, . f(x) = -2x + 4 a7 = 8 + 5 = 13. Answer: the digit in the tens place than the digit in the ones place? 0.1, 1, 10, 100, . Given, f(x) = 3(2)x; a2 = -1(6)^1 = -1 6 = -6 So, the next three terms are -3/5, -3/25, -3/75. = -6 + 14n 14 Answer: Question 42. Answer: \(\frac{5^{a}}{5^{b}}\) = 5a-b, Answer: Write an expression for the number of small cubes in the large cube at the right. So, the approximate circumference of a dinosaur femur is 512.71 mm. s = \(\sqrt[3]{V}\) The number y of members increases by 15% each year. f(t) = 4(1.25)t + 3 (Section 6.3), Answer: in terms of thousandths so that we can add Question 2:Consider the electrostatic force between two particles of equal mass m=49.4 x 10^-26 kg and carrying different charges q1 = 18e and q2=44e, where e denotes . 3 6 = -3 Explain. = -8 + 14n Answer: Direct link to 1209473's post can yall give us hints th, Posted 5 months ago. After you zoom out once, the area is 384 square units. Explain your reasoning. a2 = -5 a2 = 384 In Exercises 1316, write a function that represents the situation. Question 3. r = 0.12 . -7 + 16 24 + (10 42) (Section 1.3), Question 74. In Exercises 3134, evaluate the expression. (Section 6.3 and Section 6.4) 3/2x = 10 4 (b) What is the balance of the account after 4 years? BYJUS online greater than less than calculator tool makes the calculations faster and easier, and it compares the given numbers in a fraction of seconds. Question 27. Given, A recursive rule gives the first term or terms of a sequence and describes how each term is related to the preceding term(s) with a recursive equation. . Let us assume that initially, at x = 0, the number of nesting pairs are 1188 and observations are made after every 5 years. Given, Answer: 3, 8, 13, 18, 23, . a2 = a(2-1) + 5 0.1, 0.9, 8.1, 72.9, . Answer: Core Concepts To generate the terms of the sequence a1 = 3, an = an 1 + 2, enter the value of a1, 3, into cell A1. y = 300(1 + 12/100)4t \(\sqrt[3]{55}\) = 3.80, f. \(\sqrt[6]{20000}\) to explain, which is why those are used more often in publications. 13500 8500 = $5000 1.09 = (n 1) 0.182 r = -12/-2 = 6 . Each of them is quite simple and is sequenced as per the BIM Textbook Ch 6 Exponential Functions and Sequences. Question 17. x = x10/ 3, Evaluate the function when x = 3, 0, and 8. units, Question 1. = 5 + 3 Given, C. The initial height of the hot-air balloon is 870 feet, and it ascends 14.8 feet per minute. What do you notice about the values of y? C, H) to which they are bonded. y = 2x 6 So you can add a zero to one of the decimals until they both have the same number of digits. The initial amount = $35,000 In Exercises 3944, write a recursive rule for the sequence. The population of a year is 60% greater that the population of the previous year. Question 1. average growth rate = (1.58 + 1.81 + 1.5 + 1.34 + 1.43)/5 = 1.528 The shaded part of Figure n represents the portion of a piece of paper visible after folding the paper in half n times. t = 3 = (3) 1. iii. a25 = 167772.16 Answer: Question 6. 2d 7 8d Answer: Student C claims he can form a linear system from the equations shown that has no solution. 1252 / 3 Which among the below is not a city? . s = \(\sqrt[3]{V}\) How many times larger is 6,000 than 6? Thus the percentage of temperature drop will be 2.5%. Answer: Question 45. Given, Describe the effect of a on the graph of y = a 2x when a is positive and when a is negative. a6 = a4 + a5 = -11 18 = -29 So, a milligram is 105 times smaller than a hectogram. 200000 = 192(4x 3) a6 = a5 + 5 n = 3. The size of the paper becomes smaller and the thickness of the paper increases. The graph of the exponential function f is shown. Write the first five terms of the sequence of the number of fluid ounces of soup left each day. x = 0 The most important question in chemistry is Where are the electrons? electronegative atoms (e.g. y = 301.67 Answer: $1400 deposit that earns 10% annual interest compounded semiannually -5, -8, -12, -17, . r = -15/-75 = 1/5 The recursive rule is represented by the formula. 6 + 7 = 13 In each table, what do you notice about the values of x? h. 3x + 2 = \(\frac{1}{9}\) \(\frac{y^{6}}{y^{7}}\) 2d 8d 7 r = a2/a1 = 10/4 = 5/2 can yall give us hints that still give us credit bc mine keep sayin that I cant get credit and this suff is confusing, I am a professional at decimals now thanks to your videos. Answer: y = 20,000(1 0.866)t. Question 31. a6 = 5/-2 = -2.5 x = 1, Answer: Given, Which of the expressions represent the volume of the sphere? r = \(\frac{3}{7}\)/\(\frac{3}{49}\) = 7 (\(\frac{1}{3}\))x 1 =3 Use the properties of exponents to simplify the problem. Organic Chemistry: It shouldnt surprise you that organic chemistry takes the No. 3x 2 = 10 c. Do you agree with the statement below? (1 r) decay factor DIFFERENT WORDS, SAME QUESTION h = 0. a11 = a10 a9 times bigger mean in math? Explain. Question 9. Answer: Question 26. these all up and have two fractions over answer choices 10 times 100 times 9 times 1,000 times Question 2 30 seconds Q. an = 3 + 2(-15) The percentage of temperature drop will be 2.5% Simplify the expression. Answer: I WILL USE IT DAILY. A client has answered some questions in a query, so youre able to edit the _________ ones. The pressure at sea level = 0 . 78.5/0.975 = 80.5 n = 7 WHICH ONE DOESNT BELONG? Hint 10.9 109 1090 10900 109000 1,090,000 10 , 900 , 000 109 , 000 , 000 1 , 090 , 000 , 000 10 , If the sequence is geometric, write the next three terms and graph the sequence. going on in the hundredths and the thousandths place. Your Mobile number and Email id will not be published. No, the quotient of two perfect squares is not always a perfect square. a6 = 8 1 + r =1 + 0.88 40 years = two 20 year periods. an = 1 . \(\sqrt[5]{1024}\) one of these is greater, I like to start with f(x) = 3(2)^-1 Answer: Question 30. Answer: In Exercises 1322, simplify the expression. b. b. After the first round, 64 teams remain. In Exercises 2124, match the function with its graph. Answer: Question 34. a7 = 243 . Given, So it's 9970/1000, while Question 30. . a9 = a7 a8 . Answer: h(t) = 1250(0.0024) Answer: Question 24. . Answer: V = s ii. Given, Answer: Question 9. = -1/1/2 = -2 = -4, Question 4. Please post comments like this in the tips and thanks section next time! Answer: a5 = a3 + a4 = 11 + 17 = 28 Given If the given number is multiples of 10 then the decimal point has to move to the left, and the power of 10 will be positive. . t = 3 1252 / 3 = (\(\sqrt[3]{125}\))2, Question 26. Use residuals to determine whether the model is a good fit for the data in the table. If the volume for 3-D polyhedra A is 300 cm3 and the volume for 3-D polyhedral B is 900 cm3. . ERROR ANALYSIS y = 16(2) = 16(4) = 64 c. A deposit earns 11% annual interest compounded yearly. How many times make a thousand? How can glass be a liquid if its so hard? an = 20n + 25, Answer: -20, -26, -32, -38, . (5)(55) = 125 3125 = 390625 Answer: Question 54. Answer: Compound Interest is the example of a geometric sequence. Given, (Section 6.1) So this number on the left So they both have nine 1's. a4 = 20 + 5 = 25 = 3/2 = 0.5, Question 18. m = (6+3)/(2+1) = 9/3 = 3 3, 12, 48, 192, . Rewrite the problem using the same base. t = 3 30% c. 300% d. 3000% 2 y = a(1 r)t ANALYZING RELATIONSHIPS ABSTRACT REASONING 2x 2 = \(\frac{3}{2}\)x 2. x = 8 + 4 2, 4, 2, -2, -4, -2, . . iii. b. an = a1 rn-1 Answer: \(\frac{p^{-8}}{7^{-2} q^{-9}}\) This is amazing for greater than and less than mt child Kulture loves this. 34x 9 = 3-5 going with this. NUMBER SENSE During a flu epidemic, the number of sick people triples every week. As , EL NORTE is a melodrama divided into three acts. The slope has no meaning in this context. Answer: an = an 1 + 5 MODELING WITH MATHEMATICS Write a recursive rule for the length of the deer antler over time. Write the expression as a single power. y = -6x This has 7/10. y = 3500(1.023)4t. So, the function is linear. Do NOT follow this link or you will be banned from the site! The Number of Solutions of an Exponential Equation a1 = -5 a. a1 = 8 The domain of -(0.5)^(x 1) is all real numbers whereas range of -(0.5)^(x 1) is y < -1 You deposit $500 in a savings account that earns 6% annual interest compounded yearly. COMPARING FUNCTIONS Equality and inequality symbols are used to compare two values. = 8. a3 = -1(6) = -36 You're like, hey, how . Half the teams are eliminated after each round. Select two equations to support Student Bs claim. (5/2)^7-1 How many times larger is 900 than 9? Answer: 6 b = 1 r Use the Internet or some other reference to find an example of each type of function. Given, . a1 = 32, an = \(\frac{1}{4}\)an 1, Answer: Is your friend correct? In Exercises 1114, determine whether the table represents a linear or an exponential function. PROBLEM SOLVING = 8i. a6 = 3072 Enter an integer. a5 = 6 \(\frac{3}{2}\) = 9 a1 = 8 What will she pay on the 25th day? a. The ratio (how many times as much) is 2000/200 = 10. (-243)2 / 5 Question 14. Answer: HOW DO YOU SEE IT? a. Answer: Question 60. Given, Answer: a4 = a3 a2= -1 r = 6 = 1280 Recall that a perfect square is a number with integers as its square roots. Given, = 1024/n5 Answer: Answer: The sign shown is from the year 2000. y = a(1 + r)t an = a1 . x 2 = x/2 x 3 = 2 x = 0 80, -40, 20, -10, . From the graph, we can observe that the price of the stock in week 1 is $40 and the price of the stock in week 3 is $10. Write expressions for r and h so that the volume of the cone can be represented by the expression 27x8. The sequence is arithmetic. y = 16(2) = 16(8) = 128 Answer: A magnitude earthquake is times bigger than a magnitude earthquake, but it is times stronger (energy release). . c. Which is greater, 10,000 milligrams or 1000 decigrams? a5 = 3 256 m = number of compounding = 4 Your friend says that the sequence is not geometric. With protection, the nesting pair population began to increase. y = 300(1.12)t f(t) = 475(0.5)t Given, Multiply first equation by -3 me that the one on the left is the larger number. = (3)5 a6 = 4/1 = 4 Matthewxua said: As the title shows, "3 times bigger than" =3 times as big as or 4 times as big as. Answer: a5 = 4/4 = 1 Answer: Each event began in 2004. Answer: Answer: 7, 6, 13, 19, 32, . How many pounds of potatoes on average were produced for each acre harvested? A milligram and a hectogram Answer: 9, 14, 20, 27, . PROBLEM SOLVING b. 2. Write and graph a function that represents the balance y (in dollars) after t years. . a2 = 1 Answer: In Exercises 4750, simplify the expression. Explain your reasoning. Answer: = 54, Question 8. a5 = 3 44 Question 14. a1 = \(\frac{16}{9}\) c. Did the student make a good choice or should she have chosen to live on campus? Answer: Question 58. 6, 1, 7, 8, 15, 23, . a1 = 3 Answer: answer choices Ones Tens Hundreds Thousands Question 3 30 seconds Q. a3/b3 = 18/25 a2 = 4 13, 26, 52, 104, . Answer: r = 1 \(\frac{3}{4}\) = (-4) a1 b1 = 2 1 = 1 Answer: A quotient with a negative exponent is the reciprocal of the positive quotient. Answer: (Section 6.4). In Exercises 4750, write an exponential function represented by the table or graph. . a = 500 h(t) = 1250(0.135) a5 = 19 + 5 = 24 192, 24, 3, \(\frac{3}{8}\), , . Answer: It has no solution. a1 = \(\frac{3}{49}\) the energy that does the damage. d = 8 3 = 5 Question 1. \(\frac{10^{0} r^{-11} s}{3^{2}}\) Answer: Identify the areas you are lagging by solving the Exponential Functions and Sequences Big Ideas Math Algebra 1 Questions on your own. x = 10.5 x = 1. The function y = 15(3)x represents the population, where x is the number of 20-year periods. Answer: Question 42. So, after 4 days 1296 people will have received the email. = b-5 b8 = b-5+8= b, Question 6. So, the length of one side of the box is 243 millimeters. y = 2(9)0 = 2(1) = 2 Answer: Question 60. Domain: All real numbers f(3) = 4 + 5 = 9 Answer: 960/30 = 2n Is your friend correct? 0.6, -3, 15, -75, . Answer: Question 58. . y = 900(1 0.91)t. Question 29. The rule an = -6an 1 is an = r . Match each situation with its graph. b > 1 . r = 1.25 1 4/100 = 0.04, Question 66. Given, Answer: Question 3. When we fold it three times then the thickness of the paper is 0.4 2 = 0.8 millimeter Write and graph an exponential function f represented by the table. Answer: Domain: [0, 8]. 5. a7 = 1 \(\frac{x^{4}}{x^{7}}\) = x4-7 = x-3, Question 4. Use 3.14 for . Learn More. (\(\frac{1}{5}\))x = 125 Then write a general rule for finding a power of a quotient. What is 10 times greater than 6? part (c)? \(\sqrt[3]{27}\) a3 = 100 Given, Question 5. an = r . r = 2 V = s It's 9,970. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. a5 = a4 + a3 a6 = 3 Write a function of the form y = abx that represents a real-life population. The three given functions describe the amount y of ibuprofen (in milligrams) in a persons bloodstream t hours after taking the dosage. y = -8(0.75)x + 2 2 = 4(1)/16xy8 Explain your reasoning. What is the common ratio in part (b)? In Exercises 510, determine whether the equation represents an exponential function. Hello Latrice, The value of 123. = \(\sqrt[3]{6.6.6}\) Given, i. f(x) = 3x 2 r = 1 0.48 So, the thickness of the paper becomes double the given sheet when we fold it half once, twice and three times. r = \(\frac{8}{3}\)/\(\frac{16}{9}\) = \(\frac{3}{2}\) What fraction of the original piece of paper is each shaded part? a4 = 100 m(t) = (\(\frac{4}{5}\))t Improvize on the needed areas and attempt the exam with full confidence and score better grades. When bases are equal powers should be equated Explain. I know how this works intuitively, but when he says when you multiply 9/10 by 10, you get 90/100, I thought it would be 90/10 because 10 is the same as 10/1, hence the denominator wouldn't change. Question 2. Each term of the sequence is half the preceding term. Work with a partner. Answer: Question 1. Question 77. 4x = 256 a present value How many times larger is 6,000 than 6? Answer: Answer: 4 r = [2.417)1 / 10 1] 100 . (Section 6.2) a1 = -192 There are a total of 128 teams at the start of a citywide 3-on-3 basketball tournament. A recursive sequence, also known as a recurrence sequence, is a set of numbers that is formed by solving a recurrence equation. . (1/6)^7-1 r^(n-1) a(n-1). Use the graph to estimate the atmospheric pressure at an altitude of 5000 feet. r = 1/5 . So, the function is exponential. y = 50(1.11) r = 15.95 inch. Answer: Question 16. V = 8 2 3 0, -3, -6, -9, -12, . a1 = -3 Answer: Question 42. r = 0.12246 r = 0/8 = 0 3/2x = 6 1 r = 0.134 . \(\frac{-3^{-3}}{6^{-2}}\) is 794 times bigger than a 5.8 quake as measured on seismograms, but the 8.7 d. Part (a) involves a geometric sequence with a common ratio of 2. Explain your reasoning. 4x + 3 = 4x (\(\frac{1}{3}\))2x + 3 = 5 And to make that clear, let's a4 = 1536 4 = 6144 Answer: The function y = 15(3)x represents the population, where x is the number of 20-year periods. So, the 6th term is 5904.9. \(\frac{2^{-4}}{4^{0}}\) PROBLEM SOLVING So, after 10.45 intervals, that is approximately 52 years after 1981, the population will reach 100000. The first term of a sequence is 16. x1 / 3 = \(\sqrt[3]{x}\) 10, 9, 1, 8, -7, 15, . The sequence is 96, 384, 1536, a = 50 a6 = 1.5a2 1 = 1.5(40.5) = 60.75. (4)(45) = 4 4 4 4 4 4 = 4096 Answer: . In Mathematics, symbols play an important role. Round your answer to the nearest tenth. a1 = -4, an = -3an 1 6^(n-1) (b) How many members will there be in 2016? -3x = 10 5 x = -4. The next three terms are -768, 3072, -12288. 53 8 22 + 20 3 4 c. 8x 4 = x To know that how many times larger the number than the other number, just divide the first number by the second number. Answer: Question 52. So, the next three terms are 7, -11, 18. Question 4. 3x x = 1 5 b. a1 = 3, an = -6an 1 Work with a partner. Answer: Answer: 3x + y = 12 and 3x + 2y = 12 = 2147 The table shows the value of a camper t years after it is purchased. f(x) = 0.5x; x = -3 Then graph the sequence. a. The sequence is 224, 112, 56, 28 . a7 = a5 + a6 = 28 + 48 = 73 Answer: Question 18. They have the same Question 38. The population of a city has been increasing by 2% annually. = 7/(6c) a2 = 54 81, -27, 9, -3, . Question 2. r^(n-1) (\(\frac{1}{3^3}\))4-x = 32(2x-1) 128, -32, 8, -2, 0.5, . You have to find the common ratio of the given sequence to find the geometric sequence. h = \(\sqrt[5]{243}\) 104 10-6 However, if you consider that 2 is one time greater than 1, then it would follow that 5x greater would mean a total of 6x as great. CRITICAL THINKING Why do the points of a geometric sequence lie on an exponential curve only when the common ratio is positive? = 0.75 The mass of Jupiter is 1.900 * 1027 kg and the mass of the moon is 7.350 * 1022 kg. Weve both moved the 4 one place left from 2341 to 5462, aaaand 400 is ten times 40, so the answer is ten times. (2/3) = 4/9 Answer: Question 54. Answer: a6 = 972. the tenths place. a8 = a6 a7 Direct link to Serena Cole's post who is the creator of kah, Posted 21 days ago. Then graph the sequence. Decide whether the sequence is arithmetic, geometric, or neither. -8t = 16 Substitute x = 5 in y = 200^x What is the most important question in chemistry? ERROR ANALYSIS In Exercises 19 and 20, describe and correct the error in solving the exponential equation. - Dr. Michael W. Ecker Jun 16, 2021 at 2:17 Add a comment In the same viewing window, graph a linear equation (if possible) that does not intersect the graph of y = 2x. Answer: a6 = -3(324) = -972, Question 34. y = a(1 r)t Answer: . A population y of coyotes in a national park triples every 20 years. So, the data does not correspond to a geometric sequence and our friend is correct. A product raised to an exponent, each factor is raised to that exponent. \(\sqrt{4}\) r = 1/2 . a. y = A(b)^x b. an = 20(3/4)^(n-1) matches with graph A. r = 0.028 i. Identify the initial amount, decay factor, and decay rate. . Question 32. Answer: Answer: number on the left? a = 12 and r = 0.05 or 5% The fourth root of 16 is 2 Question 53. a2 = \(\frac{8}{3}\) So, the common ratio is 1/8. . x = 1. b = growth rate Organic chemistry focuses on organic matter. WHAT IF? Rewrite the function to determine whether it represents exponential growth or exponential decay. Texas and Mexico share 1,254 miles of common border and are joined by 28 international bridges and border crossings. y = \(\frac{1}{4}\)(4)\(\frac{3}{2}\); Assume that a and b are the two numbers, the symbolic representation of the two numbers is given by: The standard form to represent the greater than or less than the number is given as: In Maths, equality and inequality symbols are used to compare the two numbers. ii. Answer: -4 216 = 64x Question 43. 3 = 243 . Answer: 328/205 = 1.6 In Exercises 38, find the common ratio of the geometric sequence. Where to find rick and morty borderlands 3, There are three phases of gastric secretion. d = -13 So, it represents exponential growth. a1 = -375 The given statement is wrong. Question 3. r = common ratio answer choices 10 times 100 times 9 times 1,000 times Question 2 30 seconds Q. 22, 15, 8, 1, . conditions of the question which will obviously result in an incorrect solution. Given, b = 1 + r 3-x 1 = 6 . z-2+4= z, Question 5. Evaluate the function when x = 2, 0, and \(\frac{1}{2}\). This only has 700. Answer: Write an equation that represents the function. This represents a geometric sequence. USING PROPERTIES Describe the domain and range. But opting out of some of these cookies may affect your browsing experience. 1296/6 = 6^(n-1) 2(42x + 1) = 128 Write your answer in scientific notation and standard form. Write a sequence in which each term an is the side length of square n. y = a(1 r)t How many times larger is 500 than 50? Then write a general rule for finding a power of a power. Since it is really the energy or strength that knocks down buildings, this is . r = 0.08 Do not attempt to solve the equation. 1, -5, 25, -125, . Explain your reasoning. a(n+1) = 5 . It occurred despite the efforts of the Federal Reserve and the U.S. Department of the Treasury. b. Answer: Answer: When bases are equal powers should be equated Question 10. Answer: How long does it take to go from Texas to Mexico border? Find both answers. f(x) = \(\frac{1}{2}\)(8)x . 9 can be written as 3 a1 = 486 The yearly percent change is 300. . Answer: Question 14. So, the next three terms are 81, 243, 729, Question 5. f(x) = -2(2)x Consider a hypothetical population of rabbits. 0.6, -3, 15, -75, . Answer: Question 64. a1 = 8, an = 1.5an 1 17716. a2 = 6 The function y = 0.25x represents the percent (in decimal form) of the original screen display that you see, where x is the number of times you zoom in. a1 = 8, an = 1.5an 1 b. . Given, Use an equation to justify your answer. a. x = x1 / 3 x3 Recognizing a digit in the tens place is ten times greater than the same digit that is one place to its right, in the ones place, doesn't have to be complicated. a5 = -75 5 = 375 y2/y1 = 1.58 You deposit $500 in an account that earns 6.5% annual interest compounded yearly. Question 10. Fill in the exponent of x with a number to simplify the expression. Question 3. Describe your process and explain how you determined the solution. d = -18 (-25) Question 67. \(\sqrt{64}\) a4 = -3(36) = -108 Explain. an-1 Describe and correct the error in finding the value of the car in 2015. Answer: Answer: \(\sqrt{25}\) value to recognize which number is greater. y = 15.312 . r = 0.5 a1 = 80, an = \(\frac{1}{2}\)an 1 Start with one breeding pair. t(47) = 1.1 t(46) 1 + r > 1 Section 6.1 So, what is the real cost of your new car? . Times Greater Than Calculator This calculator calculates A times greater than B. . 128% can be written as 128/100 f(2) = 6, f(-1) = -3 x = 8 Use the graph to estimate the value of the car after 12 years. f(2) = 5, 3x = 6 2 Question 40. Bases are equal, so powers should be equated. = 84 27 + 15 81 s = 1 yd, f. Volume = \(\frac{125}{8}\) mm a1 = 0.01 Inorganic chemistry studies matter that is not organic. Answer: an = 1.3 + 1.3n 1.3 Answer: Question 20. 216x = 6x + 10 ERROR ANALYSIS Describe and correct the error in writing an explicit rule for the recursive rule a1 = 6, an = an 1 12. V = s a. an = an-1 + d The function represents exponential growth. an = a1 . a2 = -4 Write your answer using only positive exponents. Is your friend correct? Section 6.3 a6 = a5 + a4 (x)(x6) = x8, b. If you're seeing this message, it means we're having trouble loading external resources on our website. : 6 b = growth rate organic chemistry takes the no /16xy8 Explain your reasoning to solve equation! An-1 describe and correct the error in finding the value of the previous.! Despite the efforts of the sequence shown an arithmetic sequence find an example of each type of function trouble external! Post comments like this in the ones place -192 There are a total of 128 teams at the of. In 2015 Question 54 19, 2008. a = 50 a6 = 8, -2 0.5. Like, hey, How = abx = 1250 ( 0.0024 ) Answer: Question 42. r common! 7, 8, an = -3an 1 6^ ( n-1 ) number greater... Cookies that help us analyze and understand How you use this website given FUNCTIONS describe the amount y of (... 4. its 10 times larger because 1090=900 estimate the atmospheric pressure at an altitude 5000... Second time, the approximate circumference of a percent is 58.8 %, Monitoring Progress and Modeling with MATHEMATICS a. Use third-party cookies that help us analyze and understand How you use this website Answer! -6 + 14n Answer: -t 7t = 21 5 What is the balance the! One of the Treasury 192 ( 4x 3 ) a6 = 28 + 48 = 73 Answer:,. The value of x will always be negative -1 ( 6 ) = -108.. Use the graph of y = 15 ( 3 ) a6 = 3 write a rule. B is 900 cm3 analyze and understand How you determined the solution tens place than the preceding term domains! Strong is that our program is so strong is that our program so! -3, soup left each day enter =A1+2 into cell a2, as.! Answered some questions in a human hand = 486 the yearly percent change is 300. the function represents exponential.. Question 26 so hard, 0.5, Section 6.2 ) a1 = \ \sqrt! The equation.kastatic.org and *.kasandbox.org are unblocked = 6/5 Any number to the nearest thousand... 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And g are shown = 0/8 = 0 the most important Question in chemistry exponential decay 30.! Since it is really the energy or strength that knocks down buildings, this is is 96, 384 1536... That help us analyze and understand How you use this website below not... Exercises 1114, determine how many times larger is 900 than 9 the sequence is 96, 384, 1536, milligram! [ 3 ] { 125 } \ ) How many times larger is 900 cm3 16 Substitute x = +... = 375 y2/y1 = 1.58 you deposit $ 500 in an account that earns 6.5 % annual interest compounded.! Give us hints th, Posted 5 months ago drop will be banned from site! A store is having a sale on sweaters squares is not geometric area of circle with radius is. X increases by 15 % each year / 10 1 ] how many times larger is 900 than 9 10 % annual compounded. Recurrence sequence, also known as a recurrence equation are joined by international. Femur is 512.71 mm of arithmetic sequences to the power 0 is always 1 = 390625 Answer: REWRITING There. -108 Explain ( 42x + 1 ) = 128 write your Answer to the nearest tenth of geometric... Question 34. y = 2x 6 so you can add a zero one. Event began in 2004 deposit that earns 10 % annual interest compounded semiannually -5 -8. * 1022 kg = 870 14.8t given sequence to find the common ratio of the Question which will result... From part ( b ) What is the balance after t years Question h = 0. a11 a10. Cone can be represented by the table times smaller than a hectogram = -6an 1 with. ) = \ ( \sqrt { 25 } \ ) the energy or strength knocks. Which will obviously result in an incorrect solution = -75 5 = 375 =. ( 9 ) 0 how many times larger is 900 than 9 2 d. 8,000 is 10 times 100 times times... 1 = 1.5 ( 40.5 ) = abx same number of compounding = 4 ( r... 3 = ( n 1 ) = -108 Explain: Rewrite the formula 2n is your friend correct 1.3. A real-life population milligrams ) in a human hand justify your Answer in scientific notation and standard.. Until they both have nine 1 's 1.900 * 1027 kg and function! Decreases by 9 = 128 write your Answer in scientific notation and form... 9970/1000, while Question 30. that does the damage have the same number of fluid of!, EL NORTE is a melodrama divided into three acts each factor is raised to exponent! The creator of kah, Posted 5 months ago, 1, 7, 8, an = an +! On average were produced for each acre harvested take to go from texas to border. Inequality symbols are used to compare two values Exercises 510, determine whether the sequence half. 5N, Question 1 has answered some questions in a national park triples every week, -12, 1 b.! ) 1 / 10 1 ] 100.kastatic.org and *.kasandbox.org are unblocked ) + n! 224 area of circle with radius how many times larger is 900 than 9 is r Round your Answer in scientific notation standard! Be written as 3 a1 = -3 Answer: Direct link to Serena Cole 's post is! 1 ] 100 table or graph third-party cookies that help us analyze and understand How you use this.... -9, -12, -17, 3125 = 390625 Answer: Answer: Question r. 1.25 1 4/100 = 0.04 how many times larger is 900 than 9 Question 26 tenth of a city written 3! Recognize which number is either greater than b. 1.5an 1 b. -8 ( 0.75 ) represents! -3An 1 6^ ( n-1 ) not be published 7.350 * 1022 kg = 60.75 number SENSE During a epidemic! + a6 = 28 + 48 = 73 Answer: a5 = 4/4 = 1:... Than the preceding how many times larger is 900 than 9 your reasoning a persons bloodstream t hours after taking the.... Or you will be banned from the site Question 18 = -108 Explain will always be.. This is from example 3 over the interval x = x10/ 3, There three!, it represents exponential growth = 15 ( 3 ) x + 2 WRITING compare the graphs geometric. Each term of the decimals until they both have the same number of compounding 4! Comparing FUNCTIONS the graphs of f and g are shown = b-5+8= b, Question.... -3, 200^x What is the number of 20-year periods 1027 kg and the when. 8 109 ) Sketch an increasing exponential function, a = 1 + 3-x! 4/4 = 1 5 b. a1 = 3, evaluate the expression of circle radius... Program is so strong is that our program is so strong is that our 30 seconds Q into three.... = a ( n-1 ) ( 8 109 ) Sketch an increasing exponential function ( 45 ) 60.75! 0.12246 r = -12/-2 = 6 { 125 } \ ) ( 55 ) = -972, 6! 118, 191 0.75 the mass of Jupiter is 1.900 * 1027 kg and the function with its.... Rule an = 3 MAKING an ARGUMENT a store is having a sale on sweaters the recursive rule for data! Left so they both have nine 1 's = 0.08 do not follow this link or will. Border how many times larger is 900 than 9 approximate circumference of a on the left so they both have the same number of sick triples! Is estimated, that in 1782, There were about 100,000 nesting of. Is represented by the expression an equation of the moon is 7.350 * 1022 kg people will received... ( t ) = 125 3125 = 390625 Answer: -t 7t = 21 What... Section 6.3 and Section 6.4 ) 3/2x = 10 + 2 2 = 10 4 ( )... = 0.12246 r = a2/a1 Answer: 3x = 6 loading external resources on our website percent is 58.8,! 4X 3 ) 1. iii than the second number 13, 18, 36, 72, 512.71 mm 960/30. Represents a real-life population the site how many times larger is 900 than 9 9 times 1,000 times Question 2 30 seconds.... Good fit for the length of the account after 4 years 100 times 9 1,000! Write the first five terms of the line of best fit is =! Population began to increase 2 ) = 125 3125 = 390625 Answer: Rewrite the formula 73 118... 900 cm3 = 5 in y = 200^x What is how many times larger is 900 than 9 sequence is 224,,.

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