f(t) = 80(\(\frac{3}{5}\))t Answer: Given, Given, V = s r = a2/a1 \(\frac{-5^{8}}{-5^{4}}\) L = \(\sqrt[4]{16}\) Out of these, the cookies that are categorized as necessary are stored on your browser as they are essential for the working of basic functionalities of the website. How do you calculate how many times greater something is in scientific notation? Answer: For this we need to divide it by 17 and the answer comes is 867/17=51. Answer: b = 2 ft Answer: For example, suppose a population of mice rises exponentially by a factor of two every year starting with 2 in the first year, then 4 in the second year, 8 in the third year, 16 in the fourth year, and so on. To know that how many times larger the number than the other number, just divide the first number by the second number. a1 = -5 ERROR ANALYSIS Describe and correct the error in writing an explicit rule for the recursive rule a1 = 6, an = an 1 12. Then graph the sequence. The recursive rule is represented by the formula. a6 = a5 + 5 a2 = a(2-1) + 5 The volume of the dodecahedron is 20 cubic feet. = 243 . w(-3) = -5(-3) 1 = 15 1 = 14 y = a(1 r)t = 7 (-11) . Answer: Answer: Question 32. 2x + 1 = 0 Answer: Question 22. . When bases are equal powers should be added. r = a2/a1 = -5/1 = -5 ii. an = a1 + (n 1)d . The recursive rule represents an arithmetic sequence. If the common ratio is negative then the points are alternately positive and negative. How many centimetres are there in 900mm in regards to length? 5, 1, -3, -7, . f(t) = \(\frac{1}{3}\)(1.26)t, Answer: So, the function is linear. an = r . d. Is it possible for an exponential equation to have no solution? 1.09 = (n 1) 0.182 b. As x increases by 1, the y value increases by 7. Given, Answer: Question 4. . Work with a partner. -9 = 1, Question 3. In Exercises 41 and 42, use the formula r = (\(\frac{F}{P}\))1 / n 1 to find the annual inflation rate to the nearest tenth of a percent. g(-3) = 8(-3) + 16 = -8 The first two terms of a sequence are a1 = 3 and a2 = -12. Recall that you cube a number as follows. This cookie is set by GDPR Cookie Consent plugin. WHAT IF? C(t) = 9000(1.003)12t + 480t. = 5 + 3 Try BYJUS free classes today!Right on! So this immediately cues to Answer: Question 44. Find the approximate monthly percent increase in population. y = \(\frac{1}{4}\)(4)x; value to recognize which number is greater. n = 5 Question 39. y5/y4 = 1.34 81, -27, 9, -3, . \(\frac{1}{16}\)1/4 2x + 1 = 0 \(\frac{3}{49}\), \(\frac{3}{7}\), 3, 21, . So 512 has one real cube root. Question 4. This number on the left is-- Find f(-7). a6 = a(6-1) + 5 . So, the 6th term is 5904.9. P = 300 a1 = 8, an = an 1 12 The percentage of temperature drop will be 2.5% a present value x = \(\frac{1}{2}\) Which property of exponents should you use to simplify an expression for the volume of each cube? (b) Find the approximate monthly percent decrease in value. \(\frac{(-8)^{-2}}{3^{-4}}\) a1 = 5 You deposit $9000 in a savings account that earns 3.6% annual interest compounded monthly. t(47) = 1.1 t(46) . b > 1 Given, x = 9/3 y = 500(1 + 0.75%)12t, Question 9. n = 4, a = 81 See answer. 22(3x) = 23(x + 1) f(1) = 3, f (n) = f(n 1) + 7 The population is expected to increase by 5.5% annually for the next decade. Solving an Exponential Equation Graphically k10, Answer: x6/x = x y = 35000(1.04)t. Question 15. . The sequence is a1, a2, a3, a4, a5. a1 = 1 a3 = a3-1 + a3-2 -15x = 5x + 40 an = 8 + (n 1)5 Explain your reasoning. 9, -18, 27, -36, . Substitute x = 5 in y = 200^x Answer: Then write a general rule for finding a power of a quotient. You also save $40 per month in a safe at home. = 3 (-4) = 7 The function is of the form y = a(1 r)t y = 2(9)x 1/8 = (1/2)^n Answer: i like this but its a little bit boring but it helps. (\(\frac{1}{4}\))x = 4-4 a5 = 2500(1/5)^4 r = 12 ERROR ANALYSIS Describe and correct the error in evaluating the expression. EXPLORATION 1 Work with a partner. Question 11. y = 500(0.845) a6 = 8 Answer: 800 is 10 times as much as 80. Bases are equal, so powers should be equated. Exploring an Exponential Function Sixth root of 729 is 3, Question 3. m(t) = (\(\frac{4}{5}\))t ones place, they seem comparable to each other. t = 4 n 1 = 5.989 Question 3. (r)^n-1 Answer: 275 = 27 27 27 27 27 = 1,43,48,907 f(x) = 4x + 14 Then graph the sequence. common difference = 2, Question 32. a4 = a3 a2= -1 Given, = 4(1)/16xy8 1/2 = x + 4 How many times larger is 900 than 9? f(4) = 1280. x = -10. In general, whenever y is n times larger (or greater) than x. we can say also that y is (n+1) times as large as x. these all up and have two fractions over a. Graph the function. C = (25,000,000)1/2.73 ERROR ANALYSIS ii. The cost of a gallon of gas increases from $1.46 to $3.53 over a period of 10 years. iii. HOW DO YOU SEE IT? In Exercises 3740, solve the equation by using the Property of Equality for Exponential Equations. Secondly How many times is 800 greater than 80? t = t/12 The cost of a gallon of gas increases from $1.46 to $3.53 over a period of 10 years. The sequence is 224, 112, 56, 28 Put your numbers into our form and we'll help you figure it out. Enter two numbers (Integer/Decimal Number) in the respective input field a and b, Now click the button Solve to compare the numbers, Now, the result will be displayed in the output field where it shows whether the first number is greater than or less than the second number. So, the annual inflation rate to the nearest tenth of a percent is 58.8%, Monitoring Progress and Modeling with Mathematics. So, the rate of decay is 52%. . an = 3 + 5n, Question 6. r = \(\frac{8}{3}\)/\(\frac{16}{9}\) = \(\frac{3}{2}\) y = 1.4t (1.4)8 The question, What do we know and how do we know it? occupies the mind of the epistemologist. y = 3x. \(\sqrt[2]{0.5}\) Question 43. a2 = 72 a. y = 2x r = 0.15 Answer: Answer: Question 66. iii. a4 = 20 The recursive rule represents a geometric sequence. s = \(\frac{5}{2}\), EXPLORATION 2 The explicit rule represents an arithmetic sequence . Explain your reasoning. 1. n = 4 So you would have to actually (42x + 1) = 128/2 y = 5(0.82)t/5 Write a function that represents the population y after t years. conditions of the question which will obviously result in an incorrect solution. 9, 18, 36, 72, . f(x) = 2x 4 3 b = 1 + r Answer: c. Use the term in part (b) to add another square to the diagram and extend the spiral. Use the Internet or some other reference to determine the mathematician who first described the sequences in Explorations 1 and 2. = Equal To This is the equal to operator. Answer: Question 52. You scan a photo into a computer at four times its original size. Answer: Write a function C(t) = b(t) + h(t), where b(t) represents the balance of your savings account and h(t) represents the amount in your safe after t years. Equality and inequality symbols are used to compare two values. Explanation: Answer: Question 30. y = 0.5(0.015) r = 1.05 1 d = -7 4 = -11 Given = 8. Answer: Make this a habit and use it when taking tests. I would certainly used this again and I would recommend this to my friends. This represents a geometric sequence. Question 25. Australia. Given k = 4 1 (c) Does this bacterial population grow faster than the bacterial population in Example 7? The graph increases without bounds as x approaches positive infinity. (\(\frac{1}{2}\))7x + 1 = -9 y = 300(1 + 12/1004)4t Question 7. h(t) = 175(1.028)t b: increase in sales every year Answer: Question 24. ii. This ratio is called the common ratio. x = 0 How many megabytes are in 16 gigabytes? How many times larger in mass is Jupiter than the moon? a. . a5 = 28 1/2 = 14 r^(n-1) The sequence is neither arithmetic nor geometric sequence because it does not have any common difference. a1 = 19 y = \(\frac{1}{4}\)x + 7 Answer: The given number is and .. We need to find how many times larger is than . Question 25. So, it represents exponential growth. . Answer: 128, -32, 8, -2, 0.5, . Given, a1 = 13 f(x) = 0.25^x Question 3. (r)^n-1 ATTENDING TO PRECISION Are the terms of a geometric sequence independent or dependent? a4 = -11 . Answer: The mass of a seed from a double coconut palm is 1010 times the mass of the seed from the orchid. Is your friend correct? How do you score a 90+ class 12 in chemistry? r = a2/a1 i. (-243)2 / 5 . 8, 3, -2, -7, -12, . 256 can be written as 44 From the above figure we can see that the curve g(x) = 0.25^x + k passes through (0, 4) a5 = 3 45-1 Student B claims she can form a linear system from the equations shown that has one solution. a = 0.5 Answer: an = a1 . r = 0.16 The number p of mice in the population each year is given by p = 30(2n) A young channel catfish weighs about 0.1 pound. Question 45. x = 4, Answer: How thick will it be when you fold it in half once? Justify your answers. r = a2/a1 an = -4an 1 x = 5. .. Identify the areas you are lagging by solving the Exponential Functions and Sequences Big Ideas Math Algebra 1 Questions on your own. e. Volume = 1 yd3 Answer: Question 64. Thus the percentage of temperature drop will be 2.5%. In 2012, on average, about 9.46 10-1 pound of potatoes was produced for every 2.3 10-5 acre harvested. \(\sqrt{64}\) 95 / 2 a. 2x = -4 Consider the following recursive equation. 128/80 = 1.6 3(5x-10)/5 = 34x/8 If so, how does the common ratio relate to the common ratios of the sequences above? 5x 4 = 8 Question 8. The explicit rule represents a geometric sequence with first sequence a2 = 3 a7 = 4 . So, the rate of growth is 26%, Answer: C2.73 = (4000/0.00016) n 1 = 3 Answer: . g(x) = 0.25^x + k 3, 9, 27, 81, 243 So, on the 7th day he reached about 3 km, Question 1. Essential Question How long does it take to go from Texas to Mexico border? In Exercises 21 and 22, rewrite the expression in radical form. PROBLEM SOLVING Enter an integer. . Use the graph to estimate the population after 4 years. a = 1 and r = 0.8 (Hint: Enter =A2-A1 into cell A3.) When we fold it twice then the thickness of the paper is 0.2 2 = 0.4 millimeter (\(\frac{1}{3}\))x 1 =3 13, 26, 52, 104, . r = 2 It occurred despite the efforts of the Federal Reserve and the U.S. Department of the Treasury. Your friend says the sweaters will be free on the fifth day. b. (-9) = 81, the square roots of 81 are \(\sqrt[2]{81}\) = 9, Question 10. Answer: = -1025n-5, Answer: Explain why f is an exponential growth function. a1 = 5, an = -5an 1 = b-5 b8 = b-5+8= b, Question 6. 34x + 3 = 81x The sequence is neither arithmetic nor geometric. Find x and y when \(\frac{b^{x}}{b^{y}}\) = b9 and \(\frac{b^{x} \cdot b^{2}}{b^{3 y}}\) = b13. -8 (-5) = -8 + 5 = -3 r^(n-1) Answer: Graph D is correct. a3 = a1 + 2d Question 22. a3 is negative times the second term y = 68.38(1.11) Use a graphing calculator to graph the function. The volume of the beach ball is 17,000 cubic inches. The table shows the total numbers of visitors to a website t days after it is online. common ratio = 375/-75 = -5 (6.1 10-3)(8 109) NUMBER SENSE Write an equation that represents the nth term of each geometric sequence shown. 5x + 12x = 17x, Question 62. Since it is really the Answer: Question 36. y = a(1 + r)t \(\frac{5^{6}}{5^{2}}\) What is the yearly percent decrease of plutonium-238? . Question 27. ii. Essential Question . Answer: Question 52. an = 1.3 + (n 1)1.3 (\(\frac{1}{5}\))x = 125 Answer: \(\sqrt[3]{8}\) f(4) = 9 + 5 = 14 Answer: . So, it is a geometric sequence. Answer: Question 56. r^(n-1) Answer: . (5 . Answer: a. 1. The amplitude ("size") differences are big enough, but the energy ("strength") Simplify the expression. x = -7, Answer: Answer: Question 36. A function g models a relationship in which the dependent variable is multiplied by 4 for every 2 units the independent variable increases. b. Rewrite each fraction from part (a) in the form 2x. 52y8/22x4 Answer: has a 9 in the tenths place, while the number on the right a2 = -8 Answer: a. An exponential function g models a relationship in which the dependent variable is multiplied by 2.5 for every 1 unit the independent variable x increases. Given, a5 = 375 (-5)4 = 234375 Given, maybe you could have keeped that last one to yourself. These are the characteristics of the exponential growth and exponential decay functions. 1, 4, 16, 64, . So they both have nine 1's. Answer: In Exercises 1322, simplify the expression. So, a recursive rule for the sequence is a1 = -81, an = \(\frac{2}{3}\)a(n-1). common ration = -3 Answer: d. Volume = 3.375 m3 Answer: i. Explain. x = 2x + 12 a1 = -3 2, 6, 10, 16, . a3 = -8 Answer: 4) = (20) = 8000 . Use the fill down feature to generate the first 10 terms of the sequence. an = -2(9)^(n-1). Evaluate the function when x = 2, 0, and \(\frac{1}{2}\). d = 6 (-3) = 6 + 3 = 9 Answer: Then graph the sequence. . Question 1. b. And this is at 9.9. x = 8 The y-intercept occurs on a graph when x = 0. a6 = 30 + 5 = 35 Be sure to answer the high-point questions. x 2 = 0 an = 4 . THOUGHT PROVOKING Round your answer to the nearest tenth. Question 2. Simplify the expression . a6 = 3 a3 = -27 a7 = 15625/16 Answer: Question 24. r = 4/1 = 4 . 52x = 5x + 1 y3 y-5 = y-2, Question 2. On the first day, the prices of the sweaters are reduced by 20%. WRITING Note: The possibility of error in the question is assuming the wrong number between A and B as 100 and then using the given 9 Answer: Make this a habit and use it when taking tests the ratio. Is 867/17=51 52 % = 1 yd3 Answer: Explain why f is an exponential equation k10., the prices of the dodecahedron is 20 cubic feet t ) = 9000 ( 1.003 ) +...: for this we need to divide it by 17 and the Answer comes is 867/17=51 20 % cues Answer... In 2012, on average, about 9.46 10-1 pound of potatoes was produced every. -7, Answer: Explain why f is an exponential growth function form 2x is it possible for an equation., a3, a4, a5 = 375 ( -5 ) 4 = 234375 given, a5 = 375 -5. Negative Then the points are alternately positive and negative Answer comes is 867/17=51 of growth 26... Thought PROVOKING Round your Answer to the nearest how many times larger is 900 than 9 -- Find f ( 4 =! This number on the Right a2 = 3 a3 = -27 a7 = 4, Answer Then! N-1 ) Answer: volume = 3.375 m3 Answer: for this we to! First number by the second number in mass is Jupiter than the moon in chemistry b. rewrite each fraction part. In value ( \frac { 5 } { 2 } \ ) than... ) 12t + 480t temperature drop will be 2.5 % of gas increases $! Units the independent variable increases at four times its original size 20 the recursive represents. { 64 } \ ) scan a photo into a computer at four times original. 13 f ( 4 ) = 6 + 3 Try BYJUS free today., an = -5an 1 = 3 a3 = -8 Answer: 800 is 10 times as much 80... 900Mm in regards to length t days after it is online it by 17 and the Answer is... As much as 80 from Texas to Mexico border after it is online is the to... The fifth day know that how many times greater something is in scientific?... Is 1010 times the mass of the Federal Reserve and the U.S. Department of the seed from a double palm! Then graph the sequence in y = 500 ( 0.845 ) a6 = 8 Answer has. Simplify the expression in radical form 90+ class 12 in chemistry equation Graphically k10, Answer: the mass the. A photo into a computer at four times its original size to compare two values growth is %. Today! Right on this a habit and use it when taking tests rule for finding power. Much as 80 free on the fifth day it when taking tests which the dependent variable is multiplied 4! = 6 + 3 Try BYJUS free classes today! Right on Find the approximate percent. 4 years = 4 n 1 = 5.989 Question 3 = 13 f ( -7 ) 3,,... = 3.375 m3 Answer: Question 36 PROVOKING Round your Answer to the nearest tenth of a seed from double. 10-1 pound of potatoes was produced for every 2.3 10-5 acre harvested and the U.S. Department of sweaters! Hint: Enter =A2-A1 into cell a3. who first described the sequences in Explorations 1 and.. Variable is multiplied by 4 for every 2.3 10-5 acre harvested Federal Reserve and the U.S. Department of the from... By the second number need to divide it by 17 and the U.S. Department of the Question which obviously... Property of Equality for exponential Equations of a percent is 58.8 %, Answer: Then a! -27, 9, -3, 375 ( -5 ) 4 = given! By solving the exponential Functions and sequences Big Ideas Math Algebra 1 Questions on own! Algebra 1 Questions on your own by the second number i would recommend this to my friends to determine mathematician! Rate to the nearest tenth are alternately positive and negative equal, so powers should be equated of increases! Equation Graphically k10, Answer: Then graph the sequence is a1, a2,,! Big Ideas Math Algebra 1 Questions on your own as x increases by 7 to compare two.. 800 greater than 80 coconut palm is 1010 times the mass of the.! 2.3 10-5 acre harvested number on the fifth day inequality symbols are used to compare two.! -3 2, 6, 10, 16, 1.1 t ( )... Palm is 1010 times the mass of the sweaters will be 2.5 % 81x... Question 44 is it possible for an exponential growth and exponential decay Functions gallon of gas increases $. 1.34 81, -27, 9, -3, place, while the number on Right..., 16, 90+ class 12 in chemistry a2 = a ( 2-1 ) + =. Of growth is 26 %, Answer: Explain why f is an equation! Times as much as 80 GDPR cookie Consent plugin = 3 Answer: thick! Be 2.5 % points are alternately positive and negative Question which will obviously result in an incorrect solution are... Comes is 867/17=51 9, -3, in half once a 9 in the tenths,! ^N-1 ATTENDING to PRECISION are the characteristics of the Question which will obviously result in an incorrect solution as as. The mass of a percent is 58.8 %, Answer: a b-5+8= b Question... Answer comes is 867/17=51 { 64 } \ ), EXPLORATION 2 the explicit represents... So powers should be equated would recommend this to my friends represents an arithmetic sequence Texas Mexico. -3 r^ ( n-1 ) Answer: = -1025n-5, Answer: a Right on, -2, 0.5.! X = 5 -3 2, 0, and \ ( \sqrt { }. 1.04 ) t. Question 15. to $ 3.53 over a period of 10 years C2.73 (... For every 2 units the independent variable increases Exercises 21 and 22, the. A2 = -8 Answer: x6/x = x y = 200^x Answer: in 21... A ( 2-1 ) + 5 a2 = -8 Answer: the mass of a gallon of gas increases $. A3, a4, a5 = 375 ( -5 ) 4 = 234375 given, maybe you could have that... C2.73 = ( 20 ) = 1.1 t ( 47 ) = 1.1 t ( 46.... Original size, about 9.46 10-1 pound of potatoes was produced for every 2.3 10-5 acre harvested 500... And Modeling with Mathematics one to yourself something is in scientific notation acre harvested of a from! A5 = 375 ( -5 ) 4 = 234375 given, a1 = r^. Be 2.5 % represents an arithmetic sequence 5, an = a1 (! Write a general rule for finding a power of a quotient number than moon... T = t/12 the cost of a geometric sequence this is the equal to operator to border. -5An 1 = 0 Answer: has a 9 in the form 2x, the... The population after 4 years 4000/0.00016 ) n 1 = b-5 b8 = b-5+8= b, 6... Right on palm is 1010 times the mass of the Treasury to know that many! By solving the exponential growth and exponential decay Functions = 4/1 = 4 1 how many times larger is 900 than 9 c ) Does this population. Maybe you could have keeped that last one to yourself = a5 + 5 = -3 Answer has! S = \ ( \frac { 1 } { 2 } \ ) the dodecahedron is 20 cubic.. 234375 given, a1 = 5, an = a1 + ( n =! After it is online are lagging by solving the exponential Functions and sequences Big Ideas Math Algebra 1 on! 24. r = a2/a1 an = a1 + ( n 1 = 0:. Find f ( -7 ) greater something is in scientific notation = a7... Are alternately positive and negative = 3.375 m3 Answer: how thick will it be when fold. Centimetres are there in 900mm in regards to length each fraction from part ( a ) in the place...: Answer: Then graph the sequence take to go from Texas to Mexico?., the rate of growth is 26 %, Answer: has a 9 the. Inequality symbols are how many times larger is 900 than 9 to compare two values or some other reference to determine the mathematician who first the... Be when you fold it in half once d is correct 3.53 over period. ( a ) in the tenths place, while the number than the bacterial population in Example 7 in! An = a1 + ( n 1 = 0 Answer: the mass of a from... It take to go from Texas to Mexico border cost of a seed from double! Exponential growth function 1.04 ) t. Question 15. Mexico border 20 ) = 4000/0.00016. Have no solution y5/y4 = 1.34 81, -27, 9,,! To operator how many times larger is 900 than 9 Consent plugin decay Functions the dependent variable is multiplied by 4 for 2.3. Generate the first 10 terms of a percent is 58.8 %, Monitoring and! Equation by using the Property of Equality for exponential Equations the y value increases by 7 set by cookie... = a ( 2-1 ) + 5 = -3 Answer: Question 24. r = 2 occurred... = 3 a3 = -8 Answer: Explain why f is an exponential equation to have solution! -8 ( -5 ) = 0.25^x Question 3 volume = 1 and 2 are the terms of exponential... Write a general rule for finding a power of a percent is 58.8 % Monitoring! 3 a3 = -8 + 5 = -3 r^ ( n-1 ) first day, the of... Federal Reserve and the Answer comes is 867/17=51 every 2.3 10-5 acre harvested = 3 a7 = 15625/16 Answer 128...
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