Grade 9 · Math · Algebra 1

9th grade Exponential growth and decay worksheet

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Exponential growth and decay

Grade 9 Math Worksheet - Challenge Me

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Circle the best answer, or write your answer on the line.

Pia's robotics club grows 20% each year. One long arrow in the growth table jumps from year 0 to year 2. What number goes on that long arrow?
A used bike's value drops 10% each year, and Ren tracks it. One long arrow in the growth table jumps from year 0 to year 2. What number goes on that long arrow?
Tala's pond plant patch grows 50% each year. One long arrow in the growth table jumps from year 0 to year 3. What number goes on that long arrow?
A used scooter's value drops 20% each year, and Zee tracks it. One long arrow in the growth table jumps from year 0 to year 3. What number goes on that long arrow?
A lab sample has 192 mg of technetium-99m, whose half-life is about 6 hours. Ari reads the label. About how many mg are left after 18 hours?
A lab has 400 mg of iodine-131, whose half-life is about 8 days. Bo reads the label. About how many mg are left after 32 days?
A lab makes 3200 mg of carbon-11, whose half-life is about 20 minutes. Jun reads the label. About how many mg are left after 80 minutes?
8.
Town A has 5,000 people growing 2% a year. Town B has 4,000 growing 6% a year. Kira compares them. Which is bigger after 10 years?
- Town A
- Town B
- They are equal
9.
Town A has 8,000 people growing 1% a year. Town B has 3,000 growing 9% a year. Luz compares them. Which is bigger after 5 years?
- They are equal
- Town B
- Town A
10.
Fern patch A covers 600 square cm, growing 20% a week. Patch B covers 2,000, growing 5% a week. Noah compares them. Which is bigger after 6 weeks?
- They are equal
- Patch B
- Patch A

9th grade Exponential growth and decay worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

Exponential growth and decay. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can turn a percent rate into the factor on every arrow: 1 + r for growth, 1 − r for decay.
I can find an amount after many steps, and read the rate from a rule like y = 1200(0.85)^t.
I can find one factor for several steps and use a half-life.

Standard: F-IF.C.8b, F-LE.A.1c, A-SSE.B.3c

Words to know

exponential growth: The amount is multiplied by the same factor above 1 each step.

exponential decay: The amount is multiplied by the same factor below 1 each step.

factor (b): The number on every arrow: the new amount for each 1 you had.

percent rate (r): How much is added or taken away each step, as a percent.

half-life: The time it takes for half of a substance to be left.

Common mistakes

Your child used the percent rate itself as the multiplier, which keeps only that small part each step.

Your child used 1 plus the rate for an amount that is going down.

Your child wrote the percent as tenths instead of hundredths (5% as 0.5).

What to say

Ask: after one step, is there more or less than at the start, and by how much?

Ask: does the amount get bigger or smaller each step?

Ask: what is 5% as a decimal?

Questions parents ask

What is the most common mistake with exponential growth and decay?

Your child used the percent rate itself as the multiplier, which keeps only that small part each step.

How can I help my child with exponential growth and decay?

Ask: after one step, is there more or less than at the start, and by how much?

Are these 9th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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