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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.

Maine Learning Results learning standard: HSF.LE.A.1; HSF.LE.A.2; HSF.LE.B.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 Maine

In the Maine Learning Results, 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: Maine Department of Education

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

    Is the pattern in the table linear or exponential?

    xy
    06
    112
    218
    324
    • Exponential: it is multiplied by 6 each time
    • Neither: there is no pattern
    • Linear: it goes up by 6 each time

  2. Question 2

    f(t) = 4(2)ᵗ. What is f(1)?

    • 5
    • 8
    • 11
    • 6

  3. Question 3

    A population of 50 triples every hour. Which function gives the population after t hours?

    • P(t) = 3(50)ᵗ
    • P(t) = 50t³
    • P(t) = 50 + 3t
    • P(t) = 50(3)ᵗ

  4. Question 4

    A phone plan costs $30 plus $5 for each extra gigabyte. Which model fits best?

    • Linear
    • Exponential

  5. Question 5

    In V(t) = 1200(1.03)ᵗ, what does 1.03 tell you?

    • It starts at 1.03
    • It grows by 1.03 each time period
    • It grows by 3% each time period
    • It shrinks by 3% each time period

  6. Question 6

    f(t) = 3(2)ᵗ. What is f(3)?

    • 24
    • 18
    • 11
    • 216

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