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9th grade · Math · Unit 13 of 18

Linear or Exponential?

Add each time or multiply each time

What your child practices

Telling linear growth (add the same amount) from exponential growth (multiply by the same factor), writing exponential functions, and reading growth and decay rates.

California Content Standards learning standard: F-LE.1; F-LE.2; F-LE.5 · telling linear from exponential situations and comparing their growth

How we explain it

Children can open this short lesson before they practice.

  1. Linear: add the same amount each step.
  2. Exponential: multiply by the same factor each step.
  3. In y = a(b)ˣ, a is the start and b is the growth factor.

Example: A population of 100 doubles each year. How many after 3 years? 100 × 2 × 2 × 2. 100 × 8 = 800. Answer: 800

Sample questions

A taste of this unit. In the app, questions change every time and get easier or harder to match your child.

  1. Question 1

    A population of 500 halves every year. Which function gives the population after t years?

    • P(t) = 0.5(500)ᵗ
    • P(t) = 500t
    • P(t) = 500 + 0.5t
    • P(t) = 500(0.5)ᵗ

  2. Question 2

    The number of bacteria doubles every 20 minutes. Which model fits best?

    • Linear
    • Exponential

  3. Question 3

    In V(t) = 1200(0.97)ᵗ, what does 0.97 tell you?

    • It shrinks by 3% each time period
    • It shrinks by 0.97 each time period
    • It starts at 0.97
    • It grows by 3% each time period

  4. Question 4

    f(t) = 6(3)ᵗ. What is f(2)?

    • 324
    • 15
    • 36
    • 54

  5. Question 5

    Is the pattern in the table linear or exponential?

    xy
    05
    115
    245
    3135
    • Neither: there is no pattern
    • Linear: it goes up by 10 each time
    • Exponential: it is multiplied by 3 each time

  6. Question 6

    f(t) = 5(3)ᵗ. What is f(2)?

    • 30
    • 45
    • 14
    • 225

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