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9th grade · Math · Unit 13 of 17

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.

Alaska 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

Linear or Exponential? in Alaska

In the Alaska content standards, this is unit 13 of 17 in 9th grade Math, after Solving Systems and before Factoring & Quadratics.

Gradelings describes a child's practice on this unit as Beginning, Approaching, Meeting or Exceeding (Four practice steps). That reflects practice, not a report-card mark: the teacher decides the mark.

Source: Alaska Department of Education and Early Development

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 hour. Which function gives the population after t hours?

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

  2. Question 2

    In V(t) = 1200(1.12)ᵗ, what does 1.12 tell you?

    • It starts at 1.12
    • It grows by 1.12 each time period
    • It shrinks by 12% each time period
    • It grows by 12% each time period

  3. Question 3

    Is the pattern in the table linear or exponential?

    xy
    06
    110
    214
    318
    • Neither: there is no pattern
    • Linear: it goes up by 4 each time
    • Exponential: it is multiplied by 4 each time

  4. Question 4

    A pool fills at 40 gallons per minute. Which model fits best?

    • Exponential
    • Linear

  5. Question 5

    f(t) = 6(3)ᵗ. What is f(3)?

    • 33
    • 54
    • 5832
    • 162

  6. Question 6

    In V(t) = 500(1.05)ᵗ, what does 1.05 tell you?

    • It starts at 1.05
    • It grows by 5% each time period
    • It grows by 1.05 each time period
    • It shrinks by 5% each time period

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