Exponential Function
Alg2 - CH7 Practice Test
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}
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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
____
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
____
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.
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.
____
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
____
____
5. Evaluate log4 1 by using mental math.
16
____
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
____
c. log72x d. 2(x3 − x)
b. 2 log7x ____ x+8 x
____
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.