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Linear or exponential worksheets

Does it grow by adding the same amount, or by multiplying by the same amount? That one question separates a linear function from an exponential one, and these free printable worksheets ask it eight times a page, with an answer key.

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Linear or exponential
Linear or exponential worksheet — Tables and situations, free printable with answer key

The answer key prints on a separate page.

What's on this sheet

Half the questions are tables and half are short situations. In a table the child compares neighbors: 29, 38, 47, 56 adds 9 each time, so it is linear, and 2, 4, 8, 16 doubles each time, so it is exponential. A table that goes down counts too. 16, 8, 4, 2 halves each time and is exponential, while 16, 11, 6, 1 takes away 5 each time and is linear.

Why this sheet works

The situations ask the same thing in words, and the words are where it gets harder. A candle that burns 3 cm each hour is linear, and a pond whose lilies triple each week is exponential. The one to watch is a percent: a car that loses 10% of its value each year loses a different amount of money every year, and that is what makes it exponential.

How this one works

x: 2, 3, 4, 5 y: 16, 11, 6, 1

x2345
y161161
x2345
y161161steps−5−5−5
Linear or exponential?Linear
  1. Linear means the same amount is added or taken away each time. Exponential means the amount is multiplied by the same number each time.
  2. First check the x row: it goes up by 1 every time, so the y row can decide it.
  3. Now take the steps in y: −5, −5, −5.
  4. So y goes down by 5 every time, so the same amount is added or taken away each time.

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