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Exponential and Logarithmic Functions Practice Tests

These Grade 11 Math practice tests build fluency with exponent rules, exponential equations, logarithm definitions and properties, graph transformations, growth and decay, compound interest, and exponential models.

Skills covered

  • Using zero, negative, product, quotient, and power exponent rules
  • Solving exponential equations by rewriting with common bases
  • Evaluating logarithms and converting between logarithmic and exponential forms
  • Expanding logarithms, identifying domains, analyzing asymptotes, and transforming graphs
  • Interpreting growth, decay, half-life, compound interest, and exponential regression models

How to use these practice tests

Write the base and domain restrictions first. Use equivalent exponential or logarithmic forms, apply properties carefully, and check whether the result fits the model and its context.

For more Grade 11 Math practice, return to the Grade 11 Math category.

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Grade 11 Exponential and Logarithmic Functions Practice Tests

Practice Grade 11 Math questions about exponent rules, exponential equations, logarithms, graph transformations, growth and decay, and real-world models.

Choose the best answer. Apply exponent and logarithm properties, preserve domain restrictions, and interpret exponential models in context.

10 Questions
0/10 Questions0 %
Correct 0
Incorrect 0
Unanswered 10
1. QuestionMultiple choice

A growth factor of 1.05 represents what percent change?

Please select an answer first.

Correct answer: A

The correct answer is A 5% increase.

  1. Identify the exponential or logarithmic structure: Determine the base, exponent, logarithm, growth factor, decay factor, or graph feature involved.
  2. Apply the relationship: The growth rate is 1.05 - 1 = 0.05, which is a 5% increase.
  3. Check the result: The correct answer is A 5% increase.

The growth rate is 1.05 - 1 = 0.05, which is a 5% increase.

2. QuestionMultiple choice

A decay factor of 0.80 represents what percent change?

Please select an answer first.

Correct answer: B

The correct answer is A 20% decrease.

  1. Identify the exponential or logarithmic structure: Determine the base, exponent, logarithm, growth factor, decay factor, or graph feature involved.
  2. Apply the relationship: The decrease is 1 - 0.80 = 0.20, or 20%.
  3. Check the result: The correct answer is A 20% decrease.

The decrease is 1 - 0.80 = 0.20, or 20%.

3. QuestionMultiple choice

Approximately what is 200(1.03)2200(1.03)^2?

Please select an answer first.

Correct answer: C

The correct answer is 212.18.

  1. Identify the exponential or logarithmic structure: Determine the base, exponent, logarithm, growth factor, decay factor, or graph feature involved.
  2. Apply the relationship: Compute 200(1.03)^2 = 200(1.0609) = 212.18.
  3. Check the result: The correct answer is 212.18.

Compute 200(1.03)^2 = 200(1.0609) = 212.18.

4. QuestionMultiple choice

What is 500(0.9)1500(0.9)^1?

Please select an answer first.

Correct answer: D

The correct answer is 450.

  1. Identify the exponential or logarithmic structure: Determine the base, exponent, logarithm, growth factor, decay factor, or graph feature involved.
  2. Apply the relationship: One period of a 0.9 decay factor gives 500(0.9) = 450.
  3. Check the result: The correct answer is 450.

One period of a 0.9 decay factor gives 500(0.9) = 450.

5. QuestionMultiple choice

In A=1000(1+0.0412)12tA=1000\left(1+\frac{0.04}{12}\right)^{12t}, what is the annual interest rate?

Please select an answer first.

Correct answer: A

The correct answer is 4%.

  1. Identify the exponential or logarithmic structure: Determine the base, exponent, logarithm, growth factor, decay factor, or graph feature involved.
  2. Apply the relationship: The annual rate is the decimal 0.04, which is 4%; monthly compounding is represented by division by 12.
  3. Check the result: The correct answer is 4%.

The annual rate is the decimal 0.04, which is 4%; monthly compounding is represented by division by 12.

6. QuestionMultiple choice

What factor remains after one half-life in an exponential decay model?

Please select an answer first.

Correct answer: B

The correct answer is 12\frac{1}{2}.

  1. Identify the exponential or logarithmic structure: Determine the base, exponent, logarithm, growth factor, decay factor, or graph feature involved.
  2. Apply the relationship: By definition, one half-life reduces the quantity to half its previous amount.
  3. Check the result: The correct answer is 12\frac{1}{2}.

By definition, one half-life reduces the quantity to half its previous amount.

7. QuestionMultiple choice

If y=50⋅2ty=50\cdot2^t, when is y equal to 400?

Please select an answer first.

Correct answer: C

The correct answer is t=3t=3.

  1. Identify the exponential or logarithmic structure: Determine the base, exponent, logarithm, growth factor, decay factor, or graph feature involved.
  2. Apply the relationship: Divide by 50 to get 2^t = 8 = 2^3, so t = 3.
  3. Check the result: The correct answer is t=3t=3.

Divide by 50 to get 2^t = 8 = 2^3, so t = 3.

8. QuestionMultiple choice

If y=abxy=ab^x, which equation is linear in x after taking natural logarithms?

Please select an answer first.

Correct answer: D

The correct answer is ln⁡y=ln⁡a+xln⁡b\ln y=\ln a+x\ln b.

  1. Identify the exponential or logarithmic structure: Determine the base, exponent, logarithm, growth factor, decay factor, or graph feature involved.
  2. Apply the relationship: Taking ln gives ln y = ln(ab^x) = ln a + x ln b, a linear equation in x.
  3. Check the result: The correct answer is ln⁡y=ln⁡a+xln⁡b\ln y=\ln a+x\ln b.

Taking ln gives ln y = ln(ab^x) = ln a + x ln b, a linear equation in x.

9. QuestionMultiple choice

Approximately what is 1200(1.02)51200(1.02)^5?

Please select an answer first.

Correct answer: A

The correct answer is 1324.9.

  1. Identify the exponential or logarithmic structure: Determine the base, exponent, logarithm, growth factor, decay factor, or graph feature involved.
  2. Apply the relationship: Evaluate 1.02^5 ≈ 1.10408, then 1200(1.10408) ≈ 1324.9.
  3. Check the result: The correct answer is 1324.9.

Evaluate 1.02^5 ≈ 1.10408, then 1200(1.10408) ≈ 1324.9.

10. QuestionMultiple choice

For positive t, which grows faster: 1.08t1.08^t or 1.05t1.05^t?

Please select an answer first.

Correct answer: B

The correct answer is 1.08t1.08^t.

  1. Identify the exponential or logarithmic structure: Determine the base, exponent, logarithm, growth factor, decay factor, or graph feature involved.
  2. Apply the relationship: The larger growth factor, 1.08, produces the faster exponential growth for positive t.
  3. Check the result: The correct answer is 1.08t1.08^t.

The larger growth factor, 1.08, produces the faster exponential growth for positive t.

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