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AP Precalculus Unit 2: Exponential and Logarithmic Functions

12 questions

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Unit 2: Exponential and Logarithmic Functions

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Question 1

What is the inverse of $f (x) = 3^{x}$ ?

f^{- 1} (x) = \frac{1}{3 ^{x}}

f^{- 1} (x) = lo g_{3} (x)

f^{- 1} (x) = x^{1/3}

f^{- 1} (x) = ln (x)

Question 2

If $f (x) = 5 \cdot 2^{x}$ , what is $f (3)$ ?

30

40

125

1000

Question 3

A radioactive substance decays according to $A (t) = A_{0} \cdot (1/2)^{t / H}$ where $H$ is the half-life. If $A_{0} = 80$ grams and $H = 5$ days, how many grams remain after $15$ days?

5

gB.

10

gC.

20

gD.

40

Question 4

Solve $2^{x + 1} = 16$ for $x$ .

x = 2

x = 3

x = 4

x = 7

Question 5

Simplify $lo g_{5} (25) + lo g_{5} (125)$ using log properties.

3

5

lo g_{5} (150)

lo g_{5} (250)

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Question 6

Solve $ln (x + 2) - ln (x) = ln (3)$ for $x > 0$ .

x = - 1

x = 1

x = 2

x = 3

Question 7

A bacterial culture grows according to $N (t) = 500 \cdot 2^{t /3}$ where $t$ is in hours. By what factor does the population grow every $3$ hours?

A.Adds

500

.B.Doubles.C.Triples.D.Multiplies by

2^{3} = 8

Question 8

An investment of $\$ 2000 $g r o w sco n t in u o u s l y a t anann u a l r a t eo f$ 6% $. A ccor d in g t o$ A(t) = 2000 \cdot e^{0.06 t} $, a pp r o x ima t e l y h o w l o n g u n t i l i t d o u b l es ? (U se$ \ln 2 \approx 0.693$.)

A.About

7.7

yearsB.About

11.6

yearsC.About

16.7

yearsD.About

33.3

years

Question 9

Solve $lo g_{3} (x) = 4$ for $x$ .

x = 7

x = 12

x = 64

x = 81

Question 10

If $f (x) = e^{x}$ and $g (x) = ln (x)$ , what is $f (g (7))$ ?

0

1

7

e^{7}

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Question 11

What is the next term of the geometric sequence $3, 6, 12, 24, \dots$ ?

30

36

48

120

Question 12

Evaluate the logarithm $lo g_{2} 16$ without using a calculator.

2

4

8

16

AP Precalculus Unit 2: Exponential and Logarithmic Functions — Free with Answer Explanations | Test Practice Hub