Modeling with Functions Quiz

Grade 9 · Math · Quiz

Apply function modeling skills to real-world scenarios involving linear, quadratic, and exponential situations.

Questions

  1. A plumber charges $75 for a house call plus $50 per hour. What does the slope represent in this model?

    1. The total cost of the job
    2. The $75 flat fee
    3. The $50 hourly charge
    4. The number of hours worked
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    Answer: The $50 hourly charge

    In C(h) = 50h + 75, the slope is 50. In context, slope means the cost per additional unit of input, which is $50 per hour.

  2. Two data points on a linear model are (2, 11) and (5, 20). What is the equation of the linear function?

    1. f(x) = 3x + 5
    2. f(x) = 3x + 5
    3. f(x) = 4x + 3
    4. f(x) = 2x + 7
    Show answer

    Answer: f(x) = 3x + 5

    m = (20 − 11)/(5 − 2) = 9/3 = 3. Using point (2,11): 11 = 3(2) + b → b = 5. So f(x) = 3x + 5.

  3. A ball is launched with height h(t) = −16t² + 64t + 6. What is the height at t = 2 seconds?

    1. 6 feet
    2. 70 feet
    3. 134 feet
    4. 6 feet
    Show answer

    Answer: 70 feet

    h(2) = −16(4) + 64(2) + 6 = −64 + 128 + 6 = 70 feet.

  4. The number of social media followers triples every month starting from 100. What is the model?

    1. F(t) = 100 + 3t
    2. F(t) = 300t
    3. F(t) = 100 · 3ᵗ
    4. F(t) = 3 · 100ᵗ
    Show answer

    Answer: F(t) = 100 · 3ᵗ

    Starting at 100 and multiplying by 3 each month is exponential: F(t) = 100 · 3ᵗ.

  5. A model for the temperature T (°F) at hour h during a day is T(h) = −0.5h² + 8h + 50, where h = 0 is midnight. What does T(0) = 50 represent?

    1. The highest temperature of the day
    2. The temperature at midnight
    3. The rate of warming
    4. The number of hours of daylight
    Show answer

    Answer: The temperature at midnight

    T(0) = 50 means the temperature when h = 0 (midnight) is 50°F. It is the initial value of the model.

  6. Which data table represents an exponential function?

    1. x: 0,1,2,3 | y: 2,5,8,11
    2. x: 0,1,2,3 | y: 1,3,9,27
    3. x: 0,1,2,3 | y: 0,1,4,9
    4. x: 0,1,2,3 | y: 4,4,4,4
    Show answer

    Answer: x: 0,1,2,3 | y: 1,3,9,27

    In the table x:0,1,2,3 y:1,3,9,27, each y value is 3 times the previous (constant ratio = 3), making it exponential.

  7. In the context of modeling time (hours), it is appropriate to use negative values of t (e.g., t = −3) in the domain of the function.

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    Answer: False

    In most real-world modeling contexts, time starts at t = 0 and progresses forward. Negative time values are usually not meaningful unless the context explicitly involves time before a reference point.

  8. A car depreciates from $24,000 at a rate of 20% per year. After 1 year the car is worth $19,200. The decay factor b in B(t) = 24000 · bᵗ is __.

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    Answer: 0.8

    A 20% depreciation means retaining 80% of value each year. The decay factor b = 1 − 0.20 = 0.80. Verify: 24000 · 0.8 = 19200.

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