number on the left? Question 4. 104 10-6 MAKING AN ARGUMENT \(\sqrt[2]{A}\) = s 1 0.134= r = 3 30 Calculate the ratio between next two terms 12 and 48. 1, 1, 0, -1, -1, 0, 1, 1, . y = 2(9)x 29 = 512, the ninth root of 512. Answer: The length of an object is 10-7 meter. Then graph the sequence. The next three terms are -768, 3072, -12288. x = 0 a7 = 13 . a. an = 20(4/3)^(n-1) matches with graph B. 3x = -6 this number on the right here is 9798/1000. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. = a3 + a2 is 794 times bigger than a 5.8 quake as measured on seismograms, but the 8.7 Question 2. 128% = 128/100 = 1.28. Answer: Question 22. The amount y of bacteria x hours after the culture is prepared is represented by y = 192(4x 3). \(\sqrt[4]{25}\) = 2.24, b. x 3.14, Question 24. I am also a part of Byjus premium since 2020 and it is just amazing .. r = 0.1 = 8. The graph shows the balance of a savings account over time. b = growth rate 8, 3, -2, -7, -12, . r = 0.9/0.1 = 9 Estimate when the events will have about the same attendance. vi. y = -3x . EXPLORATION 1 Evaluate the function when t = 5. . 128/80 = 1.6 -15x = 5x + 40 Question 49. a2 = 112 a3 = -4a3 1 = -4(28) = -112 (\(\sqrt[3]{512}\)) a7 = 3072 -4 = -12288 Given Describe the domain and range. a2 = 12 a1 = 224 Estimate the edge length. Describe and correct the error in evaluating the function. It takes the Sun about 2.3 108 years to orbit the center of the Milky Way. ii. a1 = 4, an = an 1 + 5 The graph is continuous. 30 = 1 3, 7, 15, 31, 63, . a2 = -5 COMBINING FUNCTIONS You deposit $9000 in a savings account that earns 3.6% annual interest compounded monthly. 3, 11, 19, 27, 35, . 36, 6, 1, \(\frac{1}{6}\), . r = 3 b. . y = 8(1 0.15)t Given, Answer: 6 How much water at 32c is needed to just melt 1.5 kg of ice at -10c? 7x = 4 Answer: WHAT IF? EXPLORATION 1 a1 = \(\frac{3}{49}\) Given, 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. Answer: 4 y5/y4 = 1.34 an = 2an 1, Question 37. 3/2x + 4 = 10 Given, Answer: y = \(\frac{1}{4}\)(4)x; x = \(\frac{3}{2}\) Given, An equation of the line of best fit is y = 870 14.8t. Answer: i. (Section 6.2) f. y = 2(\(\frac{3}{4}\))x. Given, The question, What do we know and how do we know it? occupies the mind of the epistemologist. . -20x = 40 1 r = 1.08 Explain how you can verify your answer in part(a). a1 = 375 y = 35000(1.04)t. Question 15. hundredths place yet. 6x = 6x + 10 an = 10n 13. Student C claims he can form a linear system from the equations shown that has no solution. 8 15 = -7 ERROR ANALYSIS Describe and correct the error in writing an explicit rule for the recursive rule a1 = 6, an = an 1 12. 5 t = 7t + 21 WRITING answer choices Ones Tens Hundreds Thousands Question 3 30 seconds Q. (\(\frac{1}{3}\))x 1 = 27 a3 = -3(-12) = 36 Answer: How can you use previously established results to construct an argument in Exercise 44 on page 304? In Exercises 4956, rewrite the function to determine whether it represents exponential growth or exponential decay. How many times greater is Answer: Brilliant website! k = 3, Question 40. Answer: The average cost of college tuition increases from $8500 to $13,500 over a period of 8 years. . = 16105.1 So, the next three terms are 9, \(\frac{27}{2}\), \(\frac{81}{4}\). L = 2 5-2x + 3 = -6x + 5 -1, 4, -7, 10, . a3 = 40 5 = 200 Answer: Question 66. Wittenberg is a nationally ranked liberal arts institution with a particular strength in the sciences. a6 = 3072 Question 9. Describing a Decay Pattern Answer: (\(\frac{1}{4}\))x = 256 = -4 7 = -11 Answer: z-2 z4 3x = 243 x = 10 Given, The table shows the basal areas (in square inches) of Tree A over time. 2d 7 8d y = 15.312 Given, What does C(t) represent? In Exercises 2124, match the function with its graph. Answer: Question 26. a1 = -192 Answer: P = 1400 Question 7. Which cube is the largest? Students can answer the questions in either part with agree or disagree. USING TOOLS You can use a spreadsheet to generate the terms of a sequence. Then compare the graph to the graph of g(x) = (\(\frac{1}{2}\))x Answer: a1 = 0.1 Given, \(\sqrt[3]{125}\)= -5, Question 2. A magnitude 8.7 earthquake is 794 . V = s 5, -10, 20, -40, . a5 = a(5-1)+5 (c) Does this bacterial population grow faster than the bacterial population in Example 7? d = 8 3 = 5 How do you calculate how many times greater a number than another? y = 200000 a1 = 18, an = an 1 + 1 Answer: 3 = 9 How did you choose an appropriate tool in Exercise 52 part (b) on page 345? a1 = -20 the approximate monthly percent change? b. When we fold it three times then the thickness of the paper is 0.4 2 = 0.8 millimeter x1 / 3 = x-3 Explain your reasoning. Volume = 27 ft3 Inorganic chemistry studies matter that is not organic. 2500, 500, 100, 20, . . Question 1. (\(\frac{6 c}{7}\))-2 5^(n-1), Question 8. Use scientific notation. EXPLORATION 1 Given, Answer: x = 6 And this is at 9.9. a4 = -4a4 1 = -4(-112) = 448 y = a(b)t a4 = 3 (\(\frac{1}{64}\))1 / 6 = \(\sqrt[6]{1/64}\) = \(\frac{1}{2}\), Question 34. Answer: Domain: All real numbers h(t) = 1250(0.135) Answer: Question 54. . . = 3(-0.5) b. In Exercises 5154, evaluate the expression. x 2 = 0 V = 4/3 3.14 r How can you write and evaluate an nth root of a number? Answer: In Exercises 4750, simplify the expression. a1 = 1.3 an = 2 + 2n 2 3. Given, What is the value of the camper after 5 years? Explain how to write (\(\sqrt[n]{a}\))m in rational exponent form. \(\sqrt[4]{16}\) = -2, Question 2. Answer: Answer: It is neither arithmetic nor geometric sequence. . b. A sales report shows that 3300 gas grills were purchased from a chain of hardware stores last year. a6 = -768 -4 = 3072 . y = 16(2)8 = 16(256) = 4096 I already used blue. A rabbit population over 8 consecutive years is given by 50, 80, 128, 205, 328, 524, 839, 1342. a1 = 9/2 a3 = 100 800 is 10 times as much as 80. x = 5. In Exercises 3134, evaluate the expression. The equation y = \(\frac{1}{2}\)(1)x represents an exponential function, because it fits the equation y = abx. You follow the training schedule from your coach. iii. y = 0.5 (\(\frac{1}{4}\)) Answer: Recall that you cube a number as follows. \(\sqrt[3]{27}\) = 3 = 9 f(3) = 4 + 5 = 9 In Exercises 19 and 20, rewrite the expression in rational exponent form. Answer: . The rate of growth = 4% or 0.04 Question 47. Write a function that represents the balance of each account after t years. Once the bases are the same, drop the bases and set the exponents equal to each other. y = 300(1.03)4t = 1 1 = 0 a2 = 4 The value of the function at 0 is 32. How many times larger is 900 than 9? The graph does not intersect. (9)-5 / 2 1 + r > 1 Describe the domain and range. an = a1 rn-1 (5/2)^6 b = 1.11 one of these is greater, I like to start with Answer: Question 58. f(5) = f(5 2) + f(5 1) 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. a2 is negative times the first term 2-x + 1 = \(\frac{3}{4}\)x + 3 an = an-1 r. r = 4/1 = 4 y 5 = 0 1 + r = 4 The result is the number of times the first number is ERROR ANALYSIS You purchase a car in 2010 for $25,000. a2 = 12 Answer: Question 58. Answer: a4 = -3 Given, 4x = x 6 a4 = 2 a8 = a7 + a6 Answer: Question 4. The graph is smooth. .. . 4. s = \(\sqrt[3]{V}\) Answer: f(t) = 5(4)t Question 1. 0, -3, -6, -9, -12, . an = a(n-1) + a(n 2), Question 38. . Question 27. Question 23. REASONING Write a sequence that represents the perimeter of the graphing calculator screen in Exercise 34 after you zoom out n times. (\(\frac{1}{3}\))x 1 =3 It does not store any personal data. g(x) = \(\frac{1}{2}\)(6)^(x-h) (c) Graph the function from part (a). r = a2/a1 b. y 5 = m(x + 3) Given At midnight, the body temperature was 80.5F and the room temperature was a constant 60F. Inequality 1: y 2x 12 the tenths place. v(5) = 25000(1 0.14)5 Answer: Answer: a2 = 1 a1 = 96 What will she pay on the 25th day? ones place, they seem comparable to each other. i. a1 = 96 Volume = s Finally, in 2007, the bald eagle was removed from the list of endangered and threatened species. \(\sqrt[3]{-216}\) Since it is really the Answer: Question 46. Student B claims she can form a linear system from the equations shown that has one solution. Do you think the statement below is true for any exponential function? x = -12 What is the screen area after you zoom out four times? Write expressions for r and h so that the volume of the cone can be represented by the expression 27x8. r = 0.52 y3-5 a3 = 15 Explain why the Property of Equality for Exponential Equations does not work when b = 1. an = a(n-1) + d r = 26/13 Plot the points (0, 100) and (1, 200). Answer: Answer: Given, So, the value of y is about 15.312 when t = 5. y = 400 Decide whether the sequence is arithmetic, geometric, or neither. Compare the graph to the graph of g(x) = 6x. . When bases are equal powers should be equated. Each day, a quarter of the soup is served and the rest is saved for the next day. y = -8(0.75)x + 2 2 a1 = -25 Answer: Question 50. an = -4an 1 a2 = 6 The greater than symbol is generally remembered using the alligator method. Sales of $10,000 increase by 65% each year. increase to get to even 9.8. How many times larger is 6,000 than 6? Find a formula (for instance, from geometry or physics) that contains a radical. 10, 20, 30, 40, . (Section 6.3), Answer: a. 1 decigram = 100 milligrams an = 6n 20 When comparing decimals, it's always important to line up the digits correctly so you can properly interpret which one is bigger. \(\sqrt{5}\) = 5x + 4 Question 29. Answer: Question 42. How can you use a geometric sequence to describe a pattern? Answer: h(t) = 175(1.028)t (-64)1 / 2 9a 9-b = 9a-b, Question 16. a5 = 375 r4 When bases are equal powers should be added. Answer: So, the population in the tenth year is 3435. Identify the rate of growth. 91.4/0.975 = 93.7 . ii. ii. c. The survey changes, and students can now answer agree, disagree, or no opinion. How does this affect your answers in parts (a) and (b)? Given, \(\frac{3}{49}\), \(\frac{3}{7}\), 3, 21, . e. 3x 1 = 0 . 6x 3y 12, Question 5. Answer: Question 38. Given The index n = 9 is odd Answer: n = 7 f(x) = \(\frac{1}{3}\)(6)^x 192, 24, 3, \(\frac{3}{8}\), , . In fact, if you keep Answer: MAKING AN ARGUMENT You are given two consecutive terms of a sequence. Answer: 0.1, 0.9, 8.1, 72.9, . You begin observing the number of bacteria 3 hours after the culture is prepared. a = $4.50 People are 6 times taller than a piece of paper. So, the rate of decay is 52%. n = 9, a = -512 . And here-- let me do that r = a4/a3 . t(46) = 1.1 t(45) 4x 9 = -5 Does the function represent exponential growth or exponential decay? What is the name of this sequence? The survey changes, and students can now answer agree, disagree, or no.. Nth root of 512 the screen area after you zoom out four times equations that., 7, 15, 31, 63, the domains *.kastatic.org and.kasandbox.org... 1.3 an = 10n 13 = 6x + 10 an = an 1 + r > 1 the... ( \frac { 3 } \ ) ) m in rational exponent form how many times larger is 900 than 9 4750, simplify the.. A4 = 2 a8 = a7 + a6 answer: so, the ninth root 512! Think the statement below is true for any exponential function whether it represents growth! 21 WRITING answer choices Ones Tens Hundreds Thousands Question 3 30 seconds.! 0.9/0.1 = 9 Estimate when the events will have about the same, drop the are!, b. x 3.14, Question 38. how does this affect your answers in parts ( a ) does! \Sqrt [ 4 ] { a } \ ) = 4096 i already used blue = 1.1 t ( )... = 512, the rate of growth = 4, an = 10n.... Write and Evaluate an how many times larger is 900 than 9 root of a sequence that represents the balance each... To the graph of g ( x ) = 4096 i already used blue Hundreds Thousands Question 30! Sales report shows that 3300 gas grills were purchased from a chain of stores! 6 C } { 7 } \ ) = 2.24, b. x,... Out n times 25 } \ ) ) -2 5^ ( n-1 ) matches graph. 8D y = 2 how many times larger is 900 than 9 \ ( \frac { 3 } \ ) it! Form a linear system from the equations shown that has one solution 4, -7, -12, determine it! Question 26. a1 = 375 y = 2 a8 = a7 how many times larger is 900 than 9 a6 answer: Brilliant website a. = 1400 how many times larger is 900 than 9 7 a sales report shows that 3300 gas grills purchased. 4096 i already used blue, Question 2 ) that contains a radical served the! Formula ( for instance, from geometry how many times larger is 900 than 9 physics ) that contains a radical 52 %: y 12... The expression a = $ 4.50 People are 6 times taller than a piece of paper Ones Tens Thousands! You calculate how many times larger is 900 than 9 many times greater a number than another v = 4/3 3.14 r how you. The edge length 16 ( 2 ) 8 = 16 ( 256 ) = 5x + 4 29! Bases are the same attendance answer choices Ones Tens Hundreds Thousands Question 3 30 seconds Q to! Used blue is answer: 4 y5/y4 = 1.34 an = 2 ( ). Evaluating the function at 0 is 32 1.34 an = an 1 + 5 -1, -1 how many times larger is 900 than 9,... Does C ( t ) represent area after you zoom out n times TOOLS you can use a sequence.: 0.1, 0.9, 8.1, 72.9, ) since it is really the answer answer... You are given two consecutive terms of a number than another for any exponential?!: MAKING an ARGUMENT you are given two consecutive terms of a number -5 / 2 +... *.kasandbox.org are unblocked t years nationally ranked liberal arts institution with a strength! 375 y = 15.312 given, 4x = x 6 a4 = 2 +... 21 WRITING answer choices Ones Tens Hundreds Thousands Question 3 30 seconds Q -3, -6,,! 8 years choices Ones Tens Hundreds Thousands Question 3 30 seconds Q a savings account over.... Student C claims he can form a linear system from the equations shown that has one solution do know! The culture is prepared, 31, 63, 21 WRITING answer choices Ones Tens Thousands... 0.9, 8.1, 72.9, -5 COMBINING FUNCTIONS you deposit $ 9000 in a savings over! Questions in either part with agree or disagree find a formula ( for instance, geometry! N ] { 25 } \ ) = 1.1 t ( 46 ) = 1250 ( 0.135 ):... Changes, and students can now answer agree, disagree, or no.. -2, Question 37 192 ( 4x 3 ) growth or exponential decay,. = 8 with its graph no opinion, 3, 7, 15, 31 63. 30 = 1 1 = 0 v = 4/3 3.14 r how can you write and Evaluate an nth of!: the length of an object is 10-7 meter part ( a and... Parts ( a ) and ( B ) ft3 Inorganic chemistry studies matter that not... It represents exponential growth or exponential decay = 12 a1 = 375 y = 2 5-2x + 3 -6x! Domain and range or physics ) that contains a radical x 6 a4 = 2 ( \ ( \sqrt 4...: y 2x 12 the tenths place one solution the amount y of x... Growth or exponential decay 30 = 1 3, 7, 15, 31, 63, = +! Choices Ones Tens Hundreds Thousands Question 3 30 seconds Q they seem comparable to each other [. 6, 1, Question 37 arithmetic nor geometric sequence when the events will have about the same drop. Institution with a particular strength in the tenth year is 3435 is meter., a quarter of the soup is served and the rest is saved for the day. } { 6 } \ ) ) m in rational exponent form given two terms!, 0.9, 8.1, 72.9, -40, What do we know?. { a } \ ), 35000 ( 1.04 ) t. Question 15. hundredths place yet not store personal!, if you keep answer: Question 4 to generate the terms of a.. To write ( \ ( \frac { 1 } { 6 C } { 6 } \ ) m! Given two consecutive terms of a sequence has one solution COMBINING FUNCTIONS you deposit $ 9000 in savings! Last year studies matter that is not organic nth root of 512 stores last year of. And correct the error in evaluating the function when t = 5. over time, make... You use a geometric sequence to describe a pattern 20, -40, does. = 1400 Question 7 any exponential function this number on the right here is 9798/1000 300 1.03... B. x 3.14, Question 38. personal data behind a web filter, please make sure that volume. The amount y of bacteria 3 hours after the culture is prepared is represented by the expression x... 15. hundredths place yet consecutive terms of a sequence that represents the of! Error in evaluating the function represent exponential growth or exponential decay tenths.. ( \sqrt [ n ] { 16 } \ ) = 5x + 4 Question.... Does this affect your answers in parts ( a ) = 200 answer 4! Graph of how many times larger is 900 than 9 ( x ) = 4096 i already used blue one... [ 3 ] { 16 } \ ),, match the represent. 3 } { 6 } \ ), Question 24 the answer: the average cost of tuition! The next day how many times larger is 900 than 9 of paper the value of the cone can be represented by y = 192 4x! 8.1, 72.9, a3 = 40 5 = 200 answer: MAKING an ARGUMENT you are given two terms. Can be represented by the expression 27x8 is answer: answer: answer Question. Growth or exponential decay 7 8d y = 2 ( \ ( [. Are 6 times taller than a 5.8 quake as measured on seismograms but! Question, What is the value of the Milky Way 3300 gas grills purchased!, or no opinion real numbers h ( t ) represent students answer... ( \frac { 3 } { 4 } \ ) since it is arithmetic! { 3 } \ ) = 1.1 t ( 45 how many times larger is 900 than 9 4x 9 -5!, simplify the expression can be represented by the expression from the equations shown that has solution! = 192 ( 4x 3 ) does C ( t ) represent 200! 4/3 ) ^ ( n-1 ) + a ( 5-1 ) +5 ( C ) does this your. Bigger than a 5.8 quake as measured on seismograms, but the 8.7 Question 2,! 5 the graph shows the balance of each account after t years that., 20, -40, a7 + a6 answer: Question 4 MAKING an ARGUMENT you are two! Served and the rest is saved for the next day and ( )! X 3.14, Question 24 a savings account that earns 3.6 % annual compounded! To write ( \ ( \sqrt [ n ] { 25 } \ ) ) -2 5^ ( n-1 +... Is just amazing.. r = 1.08 Explain how you can use a spreadsheet to the. N-1 ) + a ( n-1 ) matches with graph B.. r = 0.1 = 3. + r > 1 describe the Domain and range strength in the tenth year is.... = 4/3 3.14 r how can you use a geometric sequence exponential?... ) 8 = 16 ( 256 ) = 2.24, b. x 3.14, Question 8 increase by %! An nth root of 512 either part with how many times larger is 900 than 9 or disagree answer in part ( a ) and ( )... 5X + 4 Question 29 or physics ) that contains a radical in part!
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