# Exponential Function

**Topics:**Exponential function, Natural logarithm, Logarithm

**Pages:**12 (2732 words)

**Published:**April 25, 2013

Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 1. Tell whether the function y = 2( 5 ) shows growth or decay. Then graph the function. a. This is an exponential growth function. c. This is an exponential decay function. x

b. This is an exponential growth function. d. This is an exponential growth function.

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2. Graph the inverse of the relation. Identify the domain and range of the inverse. x y

−1

4

1 2

3 1

5 0

7 1

a.

c.

Domain: {x | 0 ≤ x ≤ 4}; Range: {y | − 1 ≤ y ≤ 7} b. d.

Domain: {x | − 1 ≤ x ≤ 7}; Range: {y | − 4 ≤ y ≤ 1}

____

Domain: {x | − 7 ≤ x ≤ 1}; Domain: {x | − 7 ≤ x ≤ 1}; Range: {y | 0 ≤ y ≤ 4} Range: {y | − 4 ≤ y ≤ 0} 3. Manny is a plumber and charges $50 when he visits a client and $30 per hour for every hour he works. His bill can be expressed as a function of hours, x, with the function f(x) = 50 + 30x. Which statement explains the meaning of the inverse of the function? a. Total bill as a function of the number of hours b. Cost per hour as a function of the total bill c. Number of hours as a function of the total bill d. Total bill as a function of the cost per hour 3 4. Write the exponential equation 2 = 8 in logarithmic form. a. log38 = 2 c. log23 = 8 b. log28 = 3 d. log82 = 3

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5. Evaluate log4 1 by using mental math.

16

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a. 1 c. –2 b. 4 d. 2 4 6. Express log36 + log34.5 as a single logarithm. Simplify, if possible. a. 3 c. log310.5 b. log610.5 d. 27 7. Simplify log7x3 − log7x. a. log (x3 − x) 7

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c. log72x d. 2(x3 − x)

b. 2 log7x ____

x+8 x

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8. Solve 8 = 32 . a. x = –12 c. x = 12 b. x = 22 d. x = –22 9. The amount of money in a bank account can be expressed by the exponential equation A = 300(1.005)12t where A is the amount in dollars and t is the time in years. About how many years will it take for the amount in the account to be more than $900? a. 19 years c. 37 years b. 30 years d. 221 years 10. Simplify ln e . a. e−5 b. –5 −5x

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c. –5x d. e−5x

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11. Make a table of values, and graph the function g(x) = 3x − 3 − 2. Describe the asymptote. Tell how the graph is transformed from the graph of f(x) = 3x. a. x g(x)

1 2 3 4 5 6

−1.89 −1.67 −1 1 7 25

Horizontal asymptote y = –2; graph is translated 2 units down and 3 units to the right

b.

x 1 2 3 4 5 6

g(x) −1.89 −1.67 −2 1 7 25

Horizontal asymptote y = –2; graph is translated 2 units down and 3 units to the right c.

x 1 2 3 4 5 6

g(x) −1.89 −1.67 −1 1 7 25

Horizontal asymptote y = –3. graph is translated 3 units down and 2 units to the right d.

x 1 2 3 4 5 6

g(x) −1.89 −1.67 −1 1 7 25

1 5

Vertical asymptote x = 5; graph is translated 3 units down and 2 units to the right ____ 12. Graph the exponential function g(x) =

(2−x). Find the y-intercept and the asymptote. Describe how the graph is transformed from its parent function f(x) = 2x.

a.

y-intercept: -1, asymptote: y = 0 The graph is a reflection across the x-axis of the parent function f(x) = 2x and a horizontal compression by 1 . 5 b.

y-intercept: 1, asymptote: y = 0 The graph is a reflection across the y-axis of the parent function f(x) = 2x and a horizontal compression by 1 . 5 c.

y-intercept: − 1 , asymptote: y = 0 5 The graph is a reflection across the x-axis of the parent function f(x) = 2x and a vertical compression by 1 . 5 d.

y-intercept: 1 , asymptote: y = 0 5 The graph is a reflection across the y-axis of the parent function f(x) = 2x and a vertical compression by 1 . 5 ____ 13. Which function is vertically stretched by a factor of 3 and translated 4 units right from the parent function? a. 53x − 4 c. 3(5x + 4) b. 3 log5(x − 4) d. log5(3x + 4)

Numeric Response 14. Evaluate log44096. 15. Find the missing value if f is an exponential function. Round your answer to the nearest hundredth. x

f(x)

Matching

0 6

1 9

2 ?

3 20.25...

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