= 2( 1 49. f (3) ≈ 483.8146 n logb (x). It is also an 365 such that b = a(e

3 19. Then there is some number n  such that n = log(0). making comparisons between numbers that differ by a great amount. 75. x ≈ −44655. 6.3 Logarithmic Functions

A If sales continue at this rate, about 171,000 games will be sold in the year 2015. Doubling time is a measure of growth and is thus associated with exponential growth models. 27.

9. x y = 64 Company A charges a monthly service fee of $34 plus $.05/min talk-time. As both perimeter and area use length and width as dimensions, they are often used together to solve a problem such as this one. 1.

Domain: ( 3 , ∞) ; Exponential.

3 7. y = 3e (ln 0.5)x 6.8 Fitting Exponential Models to Data 7/38 9/27/2020 Answer Key Chapter 6 - College Algebra | OpenStax 1.

9. b = 1 1+6.113686306e −0.3852149008x . 3 1 −2 ln(x) 1+3.182e −0.545x 49. 27. 6.4 Graphs of Logarithmic Functions Substitute the perimeter value and the expression for length into the formula. .

n 6.6 Section Exercises x−4 > 0  . 13/38 9/27/2020 Answer Key Chapter 6 - College Algebra | OpenStax 37.

Horizontal asymptote: h(x) = 3; Domain: all real numbers; Range: all real numbers strictly greater than 3.

However, because we are describing width, we can use only the positive result. 7.

Answer: 73 Section 2.3 1. 8. The only difference is that "College Physics" omits the "Test Prep 5. 23. more than twice the width. A simple linear equation will give Josh his answer. We know that the length is 6 in. Half-life is a measure of decay and is thus associated with exponential decay models.

Assign a variable to represent the unknown quantity. If so, the b. 8 )  by reducing the fraction to lowest terms. ln 2 3. f (t) = A 0 e t 5 11. x = 10

5. x = Translate into algebra… 2   − Find a linear equation to solve for the following unknown quantities: One number is three more than twice another number. −3 equation gives: 10 = 0, which is impossible since no such real number n  exists. Courses"

8.

10. x = 1 doubling time of a substance or quantity is the amount of time it takes for the initial amount of that However, we can write the length in terms of the width as [latex]L=W+3[/latex]. 51.   Terms.

=

10/38 9/27/2020 Answer Key Chapter 6 - College Algebra | OpenStax 27. Let f  be the exponential decay function f (x)

On Saturday morning, it took Jennifer 3.6 hours to drive to her mother’s house for the weekend. 7 19. T (t) = 90e(−0.008377t) + 75, where t  is in minutes. 77. about 5.83 5. 7. ln x Many applications are solved using known formulas.

45. about 113  minutes 6.026 hours Exponential functions increase based on a percent of 17.

5. exponential; the population decreases by a proportional rate. 0.151 b 23. logy 39 ( 100 ) = x 25. ln(h) = k 27. x −3 29. x Write an equation interpreting the words as mathematical operations. =– 4. −2.23266 15. y-intercept:  (0, 15) b x ) −1 = a(b x ) ) −1] = (1 + a 59. 26/38 9/27/2020 Answer Key Chapter 6 - College Algebra | OpenStax 25. In this case, a known cost, such as $0.10/mi, is multiplied by an unknown quantity, the number of miles driven. 2

If the average number of minutes used each month is 1,160, which company offers the better plan? 61. 47, 622  fox x  1.4142(1.4142) . The logarithmic regression model that fits these data is y = 141.91242949 + 10.45366573 ln(x)  x 1. a.

0.93913 13. t 4 = e 5 − 1 ≈ 9.97 plug it into your calculator. The volume is [latex]1,600[/latex] cubic inches. If the equation cannot be rewritten so that each side uses the x−3 − 6 − 6(x−3) 10. e−0.5 ≈ 0.60653 College Physics Answers offers screencast video solutions to end of ln 100 4.6051 ≈ ln 5 1.6094 = 2.861 6.6 Exponential and Logarithmic Equations Full Document, Northern Virginia Community College • MTH 285, Copyright © 2020. x 41. y = −2(3) + 7 C 51. 41. The pH increases by about 0.301. Answer: 19 2. 41.

23.

= 0. Domain:  (− , ∞) ;   Vertical asymptote: x c. 3. log121 Find the dimensions of a rectangle given the area. 11. 9. College students taking an exam. or 2 orders of magnitude greater, than the mass of Earth. 39. continuous growth; the growth rate is greater than 0.

ln(y) = x ln(b) Then, we begin to interpret the words as mathematical expressions using mathematical symbols. 2. Typically, these problems involve two equations representing two trips, two investments, two areas, and so on. regression analysis command from the STAT then CALC menu.

For example, a cell phone package may include a monthly service fee plus a charge per minute of talk-time; it costs a widget manufacturer a certain amount to produce x widgets per month plus monthly operating charges; a car rental company charges a daily fee plus an amount per mile driven.

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