Exponential Growth and Decay Calculator
Model exponential growth or decay using an initial amount, percent rate, and time, with doubling-time or half-life interpretation.
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What this calculator teaches
Exponential models multiply by a fixed factor each period. Growth uses a factor greater than 1; decay uses a factor between 0 and 1.
Students see this in compound interest, population growth, bacteria, depreciation, half-life, and algorithmic growth.
Formula & Symbols
| Concept | Formula | Meaning |
|---|---|---|
| Growth | A=P(1+r)^t | Amount grows by rate r each period. |
| Decay | A=P(1-r)^t | Amount decays by rate r each period. |
| Doubling time | ln(2)/ln(1+r) | Approximate periods needed to double during growth. |
Step-by-Step Examples
- Initial amount is 1000.
- Rate is 8%, so multiplier is 1.08.
- After 5 periods: 1000(1.08)^5.
- Initial amount is 500.
- Rate is 20%, so multiplier is 0.80.
- After 3 periods: 500(0.8)^3.
Where students use this
Common Mistakes to Avoid
Convert percent to decimal before using the formula.
Exponential decay multiplies by the same percentage, not the same absolute amount.
Linear change adds. Exponential change multiplies.
Frequently Asked Questions
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Formula Explorer connections
Interpretation: This formula describes an algebraic relationship among variables, functions, equations, roots or sequences. Assumption: Respect the expression’s domain and excluded values. Check roots in the original equation because transformations can introduce extraneous solutions.