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Unit 5: Exponential and Logarithmic Functions

Study guide for CLEP CLEP College Algebra — Unit 5: Exponential and Logarithmic Functions. Practice questions, key concepts, and exam tips.

60

Practice Questions

39

Flashcards

5

Key Topics

Key Concepts to Study

exponential growth and decay
logarithm properties
change of base
natural log
solving exponential equations

Sample Practice Questions

Try these 5 questions from this unit. Sign up for full access to all 60.

Q1HARD

If f(x) = 2x2^{x} and g(x) = log2(x), which statement about the composition of functions is correct?

A.

g(f(x)) = 2x and f(g(x)) = 2x

B.

g(f(x)) = x but f(g(x)) is not defined for all x

C.

g(f(x)) = 2x and f(g(x)) = x

D.

g(f(x)) = x and f(g(x)) = x

E.

f(g(x)) = x but g(f(x)) is not defined for all x

Show Answer

Answer: D — Since f and g are inverses of each other, their composition equals the input value x.

Q2HARD

A researcher is modeling the growth of a population using the equation y = 2x2^{x}. To determine if this exponential model is appropriate, which type of plot should be used?

A.

Log-log plot with the x-axis inverted

B.

Scatter plot

C.

Semi-log plot with the x-axis logarithmically scaled

D.

Log-log plot

E.

Semi-log plot with the y-axis logarithmically scaled

Show Answer

Answer: E — A semi-log plot with the y-axis logarithmically scaled is used to determine if an exponential model is appropriate, as it will appear linear.

Q3MEDIUM

Solve the equation e2xe^{2x} = 10 for x.

A.

10/ln(2)

B.

2*ln(10)

C.

1/ln(10)

D.

ln(10)/2

E.

ln(5)

Show Answer

Answer: D — "ln(10)/2" is correct because taking ln of both sides yields 2x = ln(10), so x = ln(10)/2. Distractor B is wrong as it forgets to divide by 2.

Q4MEDIUM

A population of bacteria grows exponentially, with a growth rate of 20% per hour. If the initial population is 1000 bacteria, which equation models the population after t hours?

A.

P(t) = 1000 * (1+0.20)t−1(1 + 0.20)^{t-1}

B.

P(t) = 1000 * (1−0.20)t(1 - 0.20)^{t}

C.

P(t) = 1000 * (0.20)t(0.20)^{t}

D.

P(t) = 1000 * (1+0.20)t(1 + 0.20)^{t}

E.

P(t) = 1000 / (1+0.20)t(1 + 0.20)^{t}

Show Answer

Answer: D — Exponential growth is modeled by P(t) = P0 * (1 + r)^t, where P0 is the initial population and r is the growth rate.

Q5MEDIUM

Which of the following is an equivalent form of the exponential expression 23x+22^{3x+2}?

A.

232^{3} * 2^(2x)

B.

2^(3x) + 222^{2}

C.

232^{3} * 2^x

D.

2^(3x) * 222^{2}

E.

2^(2x) * 232^{3}

Show Answer

Answer: D — The correct option is "2^(3x) * $2^{2}$" because it applies the property of exponents that states when multiplying two powers with the same base, the exponents are added, thus 2^(3x+2) is equivalent to 2^(3x) * 2^(2).

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Study Tips for Unit 5: Exponential and Logarithmic Functions

  • Focus on understanding concepts, not memorizing facts — CLEP tests application
  • Practice with timed questions to build exam-day speed
  • Review explanations for wrong answers — they reveal common misconceptions
  • Use flashcards for key terms, practice questions for deeper understanding

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