Exponential Growth & Decay · Grades 11–11

Exponential Growth and Decay Worksheets

Population growth, radioactive decay, and compound change problems, built from whole-number quantities so every worksheet lands on a clean, exact answer.

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What it is

Exponential growth or decay happens when a quantity changes by the same PERCENT every time period, not the same amount. Growing by r% each period means multiplying by (1 + r/100); decaying by r% means multiplying by (1 − r/100).

Why it matters

Exponential change shows up everywhere outside the classroom, population models, investment growth, and radioactive half-life all follow this same pattern. Recognizing 'grows by a percent each period' as multiplication, not addition, is the key conceptual leap.

How to do it

  1. Identify the starting amount, the percent rate, and the number of time periods.
  2. Convert the percent to a growth factor: growth uses (100 + rate)/100, decay uses (100 − rate)/100.
  3. Multiply the starting amount by that factor once for each time period.

Examples by level

  • BeginnerA quantity of 32 grows by 25% each year for 1 year. What is the quantity after 1 year?40
  • IntermediateA quantity of 400 grows by 10% each year for 2 years. What is the quantity after 2 years?484
  • AdvancedA quantity of 20 grows by 50% each year for 2 years. What is the quantity after 2 years?45

Examples are generated by the same engine as the worksheets, so they're always mathematically correct. Built to avoid repeats, not reshuffle the same handful of questions.

Common mistakes

  • Adding the percent instead of multiplying by the growth/decay factor.
  • Applying the percent rate to the ORIGINAL amount every period instead of the current (already-grown) amount.
  • Confusing a growth factor greater than 1 with a decay factor, or vice versa.

Tips

  • Growth multiplies by MORE than 1 (e.g. 1.10 for 10% growth); decay multiplies by LESS than 1 (e.g. 0.90 for 10% decay).
  • The percent rate never changes, but the AMOUNT it's applied to grows or shrinks each period, that's why the increases get bigger (or smaller) over time.

For parents

Population or investment examples from the news make this concrete, ask 'is that number growing or shrinking, and by about how much each year?'

For teachers

This is conceptually close to compound interest (compoundInterest) but with the percent applied to any quantity, not just money, drawing that connection explicitly helps students transfer the skill.

Key vocabulary

growth factor
the multiplier applied each period; greater than 1 for growth
decay factor
the multiplier applied each period; between 0 and 1 for decay

Frequently asked questions

What grade is exponential growth and decay taught in?
Typically Grade 11, as part of the exponential functions strand, building on percent and exponent skills from earlier grades.
How is this different from compound interest?
The math is identical (repeated percent change) but exponential growth/decay applies to any quantity (population, mass, etc.), not just money.

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