Subscribe

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.

Arizona Academic Standards learning standard: A1.F-LE.A.1; A1.F-LE.A.2; A1.F-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 Arizona

In the Arizona 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: Arizona 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

    A candle gets 2 cm shorter every hour. Which model fits best?

    • Linear
    • Exponential

  2. Question 2

    Is the pattern in the table linear or exponential?

    xy
    01
    14
    27
    310
    • Neither: there is no pattern
    • Linear: it goes up by 3 each time
    • Exponential: it is multiplied by 3 each time

  3. Question 3

    A population of 500 triples every hour. Which function gives the population after t hours?

    • P(t) = 500(3)ᵗ
    • P(t) = 3(500)ᵗ
    • P(t) = 500t³
    • P(t) = 500 + 3t

  4. Question 4

    f(t) = 6(2)ᵗ. What is f(1)?

    • 9
    • 13
    • 8
    • 12

  5. Question 5

    In V(t) = 2000(1.1)ᵗ, what does 1.1 tell you?

    • It grows by 10% each time period
    • It shrinks by 10% each time period
    • It grows by 1.1 each time period
    • It starts at 1.1

  6. Question 6

    A population of 100 triples every hour. Which function gives the population after t hours?

    • P(t) = 3(100)ᵗ
    • P(t) = 100t³
    • P(t) = 100(3)ᵗ
    • P(t) = 100 + 3t

More 9th grade