Skip to content

Quiz: Exponential Functions

Test your understanding of exponential growth and decay, exponential functions, and compound interest with these questions.

1. What is the general form of an exponential function?

  1. f(x) = mx + b
  2. f(x) = ax² + bx + c
  3. f(x) = a · b^x
  4. f(x) = a/x
Show Answer

The correct answer is C. An exponential function has the form f(x) = a · b^x, where a is the initial value and b is the base. The variable appears in the exponent, which distinguishes it from other function types. Option A is linear. Option B is quadratic. Option D is a reciprocal/rational function.

Concept Tested: Exponential Function

See: Introduction to Exponential Functions

2. Which value of b indicates exponential decay in f(x) = a · b^x?

  1. b > 1
  2. 0 < b < 1
  3. b < 0
  4. b = 1
Show Answer

The correct answer is B. Exponential decay occurs when 0 < b < 1. The function decreases as x increases, approaching zero but never reaching it. Option A represents growth. Option C would create undefined values for non-integer exponents. Option D creates a constant function (f(x) = a).

Concept Tested: Exponential Decay / Decay Factor

See: Exponential Decay

3. A population of 500 bacteria doubles every hour. What is the population after 3 hours?

  1. 1,500
  2. 2,000
  3. 4,000
  4. 8,000
Show Answer

The correct answer is C. The function is P(t) = 500 · 2^t. After 3 hours: P(3) = 500 · 2³ = 500 · 8 = 4,000 bacteria. Option A adds instead of multiplying. Option B represents only one doubling. Option D forgets to multiply by the initial 500.

Concept Tested: Exponential Growth / Exponential Models

See: Exponential Growth

4. If a quantity decreases by 15% each year, what is the decay factor?

  1. 0.15
  2. 0.85
  3. 1.15
  4. 15
Show Answer

The correct answer is B. The decay factor is b = 1 - 0.15 = 0.85. Each year, 85% of the quantity remains (100% - 15% = 85%). Option A represents only the decrease rate, not what remains. Option C would be a growth factor. Option D is the percentage, not the decimal factor.

Concept Tested: Decay Factor / Growth and Decay Factors

See: Decay Factor from Percent Decrease

5. What is the formula for compound interest?

  1. A = P(1 + r)^t
  2. A = P + rt
  3. A = Prt
  4. A = P(1 - r)^t
Show Answer

The correct answer is A. The compound interest formula is A = P(1 + r)^t, where A is the final amount, P is the principal, r is the annual rate (as a decimal), and t is time in years. Option B is simple interest. Option C is the interest earned formula. Option D represents decay, not growth.

Concept Tested: Compound Interest

See: Compound Interest

6. In the function f(x) = 100(1.05)^x, what does 100 represent?

  1. The growth rate
  2. The growth factor
  3. The initial value
  4. The final value
Show Answer

The correct answer is C. In f(x) = a · b^x, the coefficient a = 100 is the initial value (when x = 0). The growth factor is b = 1.05. Option A would be 5% or 0.05. Option B is 1.05. Option D depends on the value of x.

Concept Tested: Initial Value / Exponential Function

See: Initial Value

7. How do you identify whether data represents exponential growth or linear growth?

  1. Check if differences between consecutive terms are constant (linear) or ratios are constant (exponential)
  2. Check if the graph is a straight line (exponential) or curved (linear)
  3. Linear growth is always faster than exponential
  4. Exponential growth uses addition; linear uses multiplication
Show Answer

The correct answer is A. Linear functions have constant differences between consecutive y-values (same amount added each time). Exponential functions have constant ratios between consecutive y-values (same factor multiplied each time). Option B reverses the graph types. Option C is false—exponential eventually surpasses linear. Option D reverses the operations.

Concept Tested: Comparing Linear and Exponential

See: Comparing Linear and Exponential Functions

8. You invest $2,000 at 6% interest compounded annually. What is the balance after 5 years?

  1. $2,600
  2. $2,676
  3. $2,300
  4. $3,000
Show Answer

The correct answer is B. Using A = P(1 + r)^t: A = 2000(1.06)^5 = 2000(1.3382) ≈ $2,676.45. Option A uses simple interest (2000 + 2000·0.06·5 = 2600). Option C has calculation errors. Option D significantly overestimates.

Concept Tested: Compound Interest / Applications

See: Compound Interest Examples

9. What is the key characteristic of an exponential function's graph?

  1. It's a straight line
  2. It has a horizontal asymptote
  3. It crosses the x-axis
  4. It has a vertex
Show Answer

The correct answer is B. Exponential functions have a horizontal asymptote (usually the x-axis, y = 0) that the curve approaches but never reaches. Option A describes linear functions. Option C is false—exponential functions with positive a never cross the x-axis. Option D describes parabolas.

Concept Tested: Graphing Exponentials

See: Key Features of Exponential Graphs

10. A car worth $25,000 depreciates by 20% per year. What is its value after 3 years?

  1. $10,000
  2. $12,800
  3. $15,000
  4. $20,000
Show Answer

The correct answer is B. The decay factor is 1 - 0.20 = 0.80. Using V(t) = 25000(0.80)^t: V(3) = 25000(0.80)³ = 25000(0.512) = $12,800. Option A subtracts 20% three times incorrectly. Option C uses simple depreciation. Option D represents only one year of depreciation.

Concept Tested: Exponential Decay / Applications

See: Applications of Exponential Functions