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9th grade · Math · Unit 14 of 16

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.

Texas Essential Knowledge and Skills (TEKS) teks student expectation: A.9(B); A.9(C) · exponential growth and decay, and writing f(x) = abˣ

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 Texas

In the Texas Essential Knowledge and Skills (TEKS), this is unit 14 of 16 in 9th grade Math, after Exponents & Powers and before Sequences.

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: Texas Education Agency (TEA)

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 200 halves every week. Which function gives the population after t weeks?

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

  2. Question 2

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

    • Exponential
    • Linear

  3. Question 3

    Is the pattern in the table linear or exponential?

    xy
    05
    19
    213
    317
    • Exponential: it is multiplied by 4 each time
    • Linear: it goes up by 4 each time
    • Neither: there is no pattern

  4. Question 4

    In V(t) = 500(1.15)ᵗ, what does 1.15 tell you?

    • It shrinks by 15% each time period
    • It grows by 15% each time period
    • It grows by 1.15 each time period
    • It starts at 1.15

  5. Question 5

    f(t) = 2(2)ᵗ. What is f(2)?

    • 16
    • 8
    • 5
    • 6

  6. Question 6

    A car's value drops by 15% each year. Which model fits best?

    • Exponential
    • Linear

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