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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.

Minnesota K-12 Academic Standards benchmark: 9.1.1.11; 9.3.7.2 · telling linear from exponential models

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 Minnesota

In the Minnesota K-12 Academic 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: Minnesota Department of Education (MDE)

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

    f(t) = 2(2)ᵗ. What is f(3)?

    • 12
    • 10
    • 64
    • 16

  2. Question 2

    A population of 200 halves every hour. Which function gives the population after t hours?

    • P(t) = 200 + 0.5t
    • P(t) = 200t
    • P(t) = 200(0.5)ᵗ
    • P(t) = 0.5(200)ᵗ

  3. Question 3

    In V(t) = 1000(0.94)ᵗ, what does 0.94 tell you?

    • It shrinks by 0.94 each time period
    • It starts at 0.94
    • It grows by 6% each time period
    • It shrinks by 6% each time period

  4. Question 4

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

    • Exponential
    • Linear

  5. Question 5

    Is the pattern in the table linear or exponential?

    xy
    03
    16
    29
    312
    • Exponential: it is multiplied by 3 each time
    • Linear: it goes up by 3 each time
    • Neither: there is no pattern

  6. Question 6

    f(t) = 6(2)ᵗ. What is f(5)?

    • 248832
    • 60
    • 192
    • 38

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