Exponential Functions Quiz

Grade 10 · Math · Quiz

Test your understanding of exponential growth, decay, graphs, and properties.

Questions

1. What is f(3) for f(x) = 2 · 3ˣ?

   1. 18
   2. 54
   3. 27
   4. 8
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   Answer: 54

   f(3) = 2·3³ = 2·27 = 54.

2. The function f(x) = 5 · (0.9)ˣ represents exponential growth.

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   Answer: False

   Base 0.9 < 1, so the function decays (decreases) over time, not grows.

3. In f(x) = a · bˣ, the value a represents the ___ value of the function.

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   Answer: initial

   f(0) = a·b⁰ = a·1 = a. So a is the initial (starting) value of the function.

4. Which is the horizontal asymptote of f(x) = 4 · 2ˣ - 3?

   1. y = 4
   2. y = 2
   3. y = -3
   4. y = 0
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   Answer: y = -3

   The -3 shifts the graph down 3, moving the asymptote from y=0 to y=-3.

5. A population of bacteria doubles every hour. Starting at 100, after 4 hours there are:

   1. 400
   2. 800
   3. 1600
   4. 200
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   Answer: 1600

   100·2⁴ = 100·16 = 1600. Each hour multiplies by 2: 100→200→400→800→1600.

6. f(x) = 3ˣ and g(x) = (1/3)ˣ are reflections of each other across the y-axis.

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   Answer: True

   (1/3)ˣ = 3⁻ˣ = f(-x). Replacing x with -x reflects across the y-axis.

7. The approximate value of the natural base e is ___.

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   Answer: 2.718

   e ≈ 2.71828... It appears in natural growth, compound interest, and calculus.

8. Which describes the end behavior of f(x) = (0.5)ˣ as x → ∞?

   1. f(x) → ∞
   2. f(x) → 0
   3. f(x) → 1
   4. f(x) → -∞
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   Answer: f(x) → 0

   As x→∞, (0.5)ˣ→0. The function decays toward the asymptote y=0 but never reaches it.

9. Exponential functions of the form f(x) = bˣ always pass through the point (0, 1).

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   Answer: True

   Any base b raised to the 0 power = 1, so f(0) = b⁰ = 1 for all valid bases.

10. A car worth $20,000 depreciates at 15% per year. Its value after t years is:

    1. 20000 · (1.15)ᵗ
    2. 20000 · (0.85)ᵗ
    3. 20000 - 15t
    4. 20000 · (0.15)ᵗ
    Show answer

    Answer: 20000 · (0.85)ᵗ

    15% depreciation means the car retains 85% = 0.85 of its value each year. Decay model: V = 20000·(0.85)ᵗ.

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