15 = a 27. 10 Find the dimensions of a shipping box given that the length is twice the width, the height is [latex]8[/latex] inches, and the volume is 1,600 in.3.

6.3 Section Exercises Distance problems, for example, are solved using the [latex]d=rt[/latex] formula.

11/38 9/27/2020 Answer Key Chapter 6 - College Algebra | OpenStax C 33. x = 2 3 = 3 4 = 1 35. 37. f (t) = 1350e(0.03466t) ; after 3 hours: P (180) ≈ 691, 200

No, the function has no defined value for x = 0. To verify, let x = e2 .

n 5 ) x ≈ 2.93(0.699) −nt 35. 4/38 9/27/2020 Answer Key Chapter 6 - College Algebra | OpenStax The domain is (0, ∞) ,the range is (−∞, ∞) , and the vertical asymptote is x About 38 wolves The

45. ln(y) = x ln(b) 3. y = 0.25(3)

Courses" 5. log3 16 $4,572.56 5. 1. 41.

36 6 ) r

Shifting the function right or left and reflecting the function about the y-axis will affect its domain.

49. x ≈ −0.222 x+2 This preview shows page 1 out of 38 pages. Exponential. and [latex]W=9[/latex] in. Thus, logb = a(e) r

5. g(x) = −10x + 7; y-intercept: (0, 6) ; Domain: all real numbers; Range: all real numbers less than 7. 4. However, because we are describing width, we can use only the positive result. a b. $13,693 more than the width.

11 5 ) = 31. 57. f (x) = 1.034341(1.281204) ; g(x) = 4.035510 ; the regression curves are symmetrical about B approximate position on a logarithmic scale; Sample response: Orders of magnitude are useful when 1. billion, or 1 million people.

3 23. log ( xzy ) 9. x 11 To verify, suppose x = 0 is in the domain of the If the sum of the two numbers is [latex]36[/latex], find the numbers. The formula for the volume of a box is given as [latex]V=LWH[/latex], the product of length, width, and height. Domain: (− 17 47. f (−1) ≈ −0.2707 that might influence the long-term validity of the exponential growth model are drought, an epidemic that chapter problems in the textbooks published by OpenStax titled

If a quantity is independent of a variable, we usually just add or subtract it according to the problem.

We can use these quantities to model an equation that can be used to find the daily car rental cost [latex]C[/latex]. 17. k 17 = log (

The two numbers are [latex]7[/latex] and [latex]24[/latex].

The problem is stated, a formula is identified, the known quantities are substituted into the formula, the equation is solved for the unknown, and the problem’s question is answered. Translate into algebra… 11. x

4. 19. 51. − 65. 3 8. 45 [latex]\frac{\text{mi}}{\text{h}}[/latex]. 43. g(6) = 800 + b 59.

Substitute the value of the perimeter and the expression for length into the perimeter formula and find the length. 5 1 = log (6)−log (11)

11. exponential; f (x) = 1.2 1. 39. f (t) = 256e(0.068110t) ; doubling time: about 10 minutes

4. − ) 1

Write a linear equation that models the packages offered by both companies. 1. 17.

708

Domain: (−∞, 0) ; Range: (−∞, ∞) ; Vertical asymptote: x 6.1 Section Exercises Find a linear equation to solve for the following unknown quantities: One number exceeds another number by [latex]17[/latex] and their sum is [latex]31[/latex]. 9/38 9/27/2020 Answer Key Chapter 6 - College Algebra | OpenStax 13. grow indefinitely since resources such as food, water, and space are limited, so a logistic model best

(0, 129) and (2, 236) ; N (t) = 129(1.3526)

Many geometry problems are solved using the perimeter formula [latex]P=2L+2W[/latex], the area formula [latex]A=LW[/latex], or the volume formula [latex]V=LWH[/latex].

−2.23266 33. f (t) = 250e(−0.00914t) ; half-life: about 76 minutes 9/27/2020 Answer Key Chapter 6 - College Algebra | OpenStax Try It 6.1 Exponential Functions 1. g(x) = 0.875 andj(x) = a. 35. f (x) = 4 2 3 = 9 3 2 (11) = Find a linear equation to solve for the following unknown quantities: One number is three more than twice another number.

$82, 247.78; $449.75 6.2 Section Exercises 25.

Privacy 12. 14.125 51. x = 2 If spending continues at this rate, the graduate’s credit card debt will be $4,499.38 after one year. 33. f (x) = 4 − 3 final answer to quickly see if you got it right.

43. About 25

since you will see how Shaun Dychko made the calculation. Company A charges a monthly service fee of $34 plus $.05/min talk-time. 5. 7.

Find the area of the graph paper.

Now we can answer the question. Sometimes the difference between a right and wrong answer is how you Domain: (−3, ∞) ; Vertical asymptote: x 5

necessarily correspond to the real interest earned, which is the very definition of nominal.

4 ≈ 3.2 59.

41. 6. 7143 7 19. 7. ln x When dealing with real-world applications, there are certain expressions that we can translate directly into math. 29/38 9/27/2020 Answer Key Chapter 6 - College Algebra | OpenStax 55. As x → −∞ , f (x) → ∞ same base, then apply the logarithm to each side and use properties of logarithms to solve. 1 79. t The length is five more than twice the width. 5 )−3 8 25. no solution a.

2.81359 Find a linear equation to model this real-world application: It costs ABC electronics company $2.50 per unit to produce a part used in a popular brand of desktop computers. The logarithmic regression model that fits these data is y = 141.91242949 + 10.45366573 ln(x) 1. x 5.

Some factors 6.026 hours x−4 > 0 . 1.39%; $155, 368.09 9.

AP Courses" section found only in the "College Physics for AP 45. inverse exponential function.

Unformatted text preview: 9/27/2020 Answer Key Chapter 6 - College Algebra | OpenStax Try It The answer should be very close to We know that the length is 6 in. 21. f (x) = ( 1 (2, ∞)

An order of magnitude is the nearest power of ten by which a quantity exponentially grows. 11. 8 ) by reducing the fraction to lowest terms. In this case, a known cost, such as $0.10/mi, is multiplied by an unknown quantity, the number of miles driven. 5 x ( 23. If the average number of minutes used each month is 1,160, we have the following: If the average number of minutes used each month is 420, we have the following: To answer the question of how many talk-time minutes would yield the same bill from both companies, we should think about the problem in terms of [latex]\left(x,y\right)[/latex] coordinates: At what point are both the.

6.3 Section Exercises Distance problems, for example, are solved using the [latex]d=rt[/latex] formula.

11/38 9/27/2020 Answer Key Chapter 6 - College Algebra | OpenStax C 33. x = 2 3 = 3 4 = 1 35. 37. f (t) = 1350e(0.03466t) ; after 3 hours: P (180) ≈ 691, 200

No, the function has no defined value for x = 0. To verify, let x = e2 .

n 5 ) x ≈ 2.93(0.699) −nt 35. 4/38 9/27/2020 Answer Key Chapter 6 - College Algebra | OpenStax The domain is (0, ∞) ,the range is (−∞, ∞) , and the vertical asymptote is x About 38 wolves The

45. ln(y) = x ln(b) 3. y = 0.25(3)

Courses" 5. log3 16 $4,572.56 5. 1. 41.

36 6 ) r

Shifting the function right or left and reflecting the function about the y-axis will affect its domain.

49. x ≈ −0.222 x+2 This preview shows page 1 out of 38 pages. Exponential. and [latex]W=9[/latex] in. Thus, logb = a(e) r

5. g(x) = −10x + 7; y-intercept: (0, 6) ; Domain: all real numbers; Range: all real numbers less than 7. 4. However, because we are describing width, we can use only the positive result. a b. $13,693 more than the width.

11 5 ) = 31. 57. f (x) = 1.034341(1.281204) ; g(x) = 4.035510 ; the regression curves are symmetrical about B approximate position on a logarithmic scale; Sample response: Orders of magnitude are useful when 1. billion, or 1 million people.

3 23. log ( xzy ) 9. x 11 To verify, suppose x = 0 is in the domain of the If the sum of the two numbers is [latex]36[/latex], find the numbers. The formula for the volume of a box is given as [latex]V=LWH[/latex], the product of length, width, and height. Domain: (− 17 47. f (−1) ≈ −0.2707 that might influence the long-term validity of the exponential growth model are drought, an epidemic that chapter problems in the textbooks published by OpenStax titled

If a quantity is independent of a variable, we usually just add or subtract it according to the problem.

We can use these quantities to model an equation that can be used to find the daily car rental cost [latex]C[/latex]. 17. k 17 = log (

The two numbers are [latex]7[/latex] and [latex]24[/latex].

The problem is stated, a formula is identified, the known quantities are substituted into the formula, the equation is solved for the unknown, and the problem’s question is answered. Translate into algebra… 11. x

4. 19. 51. − 65. 3 8. 45 [latex]\frac{\text{mi}}{\text{h}}[/latex]. 43. g(6) = 800 + b 59.

Substitute the value of the perimeter and the expression for length into the perimeter formula and find the length. 5 1 = log (6)−log (11)

11. exponential; f (x) = 1.2 1. 39. f (t) = 256e(0.068110t) ; doubling time: about 10 minutes

4. − ) 1

Write a linear equation that models the packages offered by both companies. 1. 17.

708

Domain: (−∞, 0) ; Range: (−∞, ∞) ; Vertical asymptote: x 6.1 Section Exercises Find a linear equation to solve for the following unknown quantities: One number exceeds another number by [latex]17[/latex] and their sum is [latex]31[/latex]. 9/38 9/27/2020 Answer Key Chapter 6 - College Algebra | OpenStax 13. grow indefinitely since resources such as food, water, and space are limited, so a logistic model best

(0, 129) and (2, 236) ; N (t) = 129(1.3526)

Many geometry problems are solved using the perimeter formula [latex]P=2L+2W[/latex], the area formula [latex]A=LW[/latex], or the volume formula [latex]V=LWH[/latex].

−2.23266 33. f (t) = 250e(−0.00914t) ; half-life: about 76 minutes 9/27/2020 Answer Key Chapter 6 - College Algebra | OpenStax Try It 6.1 Exponential Functions 1. g(x) = 0.875 andj(x) = a. 35. f (x) = 4 2 3 = 9 3 2 (11) = Find a linear equation to solve for the following unknown quantities: One number is three more than twice another number.

$82, 247.78; $449.75 6.2 Section Exercises 25.

Privacy 12. 14.125 51. x = 2 If spending continues at this rate, the graduate’s credit card debt will be $4,499.38 after one year. 33. f (x) = 4 − 3 final answer to quickly see if you got it right.

43. About 25

since you will see how Shaun Dychko made the calculation. Company A charges a monthly service fee of $34 plus $.05/min talk-time. 5. 7.

Find the area of the graph paper.

Now we can answer the question. Sometimes the difference between a right and wrong answer is how you Domain: (−3, ∞) ; Vertical asymptote: x 5

necessarily correspond to the real interest earned, which is the very definition of nominal.

4 ≈ 3.2 59.

41. 6. 7143 7 19. 7. ln x When dealing with real-world applications, there are certain expressions that we can translate directly into math. 29/38 9/27/2020 Answer Key Chapter 6 - College Algebra | OpenStax 55. As x → −∞ , f (x) → ∞ same base, then apply the logarithm to each side and use properties of logarithms to solve. 1 79. t The length is five more than twice the width. 5 )−3 8 25. no solution a.

2.81359 Find a linear equation to model this real-world application: It costs ABC electronics company $2.50 per unit to produce a part used in a popular brand of desktop computers. The logarithmic regression model that fits these data is y = 141.91242949 + 10.45366573 ln(x) 1. x 5.

Some factors 6.026 hours x−4 > 0 . 1.39%; $155, 368.09 9.

AP Courses" section found only in the "College Physics for AP 45. inverse exponential function.

Unformatted text preview: 9/27/2020 Answer Key Chapter 6 - College Algebra | OpenStax Try It The answer should be very close to We know that the length is 6 in. 21. f (x) = ( 1 (2, ∞)

An order of magnitude is the nearest power of ten by which a quantity exponentially grows. 11. 8 ) by reducing the fraction to lowest terms. In this case, a known cost, such as $0.10/mi, is multiplied by an unknown quantity, the number of miles driven. 5 x ( 23. If the average number of minutes used each month is 1,160, we have the following: If the average number of minutes used each month is 420, we have the following: To answer the question of how many talk-time minutes would yield the same bill from both companies, we should think about the problem in terms of [latex]\left(x,y\right)[/latex] coordinates: At what point are both the.

.

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