Exponential Functions Quiz

Grade 9 · Math · Quiz

Assess your ability to identify, evaluate, graph, and apply exponential growth and decay models.

Questions

  1. What is the y-intercept of f(x) = 3 · 4ˣ?

    1. 1
    2. 3
    3. 4
    4. 12
    Show answer

    Answer: 3

    At x = 0: f(0) = 3 · 4⁰ = 3 · 1 = 3. The y-intercept equals the initial value a.

  2. Solve for x: 2ˣ⁺¹ = 16

    1. x = 2
    2. x = 3
    3. x = 4
    4. x = 8
    Show answer

    Answer: x = 3

    2ˣ⁺¹ = 16 = 2⁴. So x + 1 = 4, giving x = 3.

  3. A car originally worth $20,000 loses 15% of its value each year. What is the value after 3 years?

    1. $11,000
    2. $12,252.50
    3. $14,450
    4. $17,000
    Show answer

    Answer: $12,252.50

    V(3) = 20000 · (0.85)³ = 20000 · 0.614125 = $12,252.50.

  4. Which of the following is the graph of an exponential decay function?

    1. Starts at (0,1) and rises steeply to the right
    2. Starts at (0,1) and falls steeply approaching y = 0
    3. A straight line with negative slope
    4. A parabola opening downward
    Show answer

    Answer: Starts at (0,1) and falls steeply approaching y = 0

    Exponential decay graphs start at a positive value when x = 0 and decrease toward the horizontal asymptote y = 0 as x increases.

  5. The function f(x) = 5 · (0.9)ˣ represents the number of bacteria (in thousands) remaining after x hours. What is the initial count?

    1. 0.9 thousand
    2. 5 thousand
    3. 0.5 thousand
    4. 5.9 thousand
    Show answer

    Answer: 5 thousand

    The initial value is f(0) = 5 · (0.9)⁰ = 5 · 1 = 5 thousand bacteria.

  6. For f(x) = 2ˣ − 3, what is the horizontal asymptote?

    1. y = 0
    2. y = 2
    3. y = −3
    4. y = 3
    Show answer

    Answer: y = −3

    The graph of f(x) = 2ˣ has asymptote y = 0. The −3 shifts the entire graph down 3 units, so the asymptote becomes y = −3.

  7. The function f(x) = (−2)ˣ is an exponential function.

    Show answer

    Answer: False

    Exponential functions require a positive base (b > 0, b ≠ 1). A negative base like −2 causes alternating signs and is not a valid exponential function.

  8. Solve: 9ˣ = 3⁴. The value of x is __.

    Show answer

    Answer: 2

    Express both sides with base 3: 9ˣ = (3²)ˣ = 3²ˣ and 3⁴. So 2x = 4, giving x = 2.

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