Exponential Growth and Decay Simulator
Visualize percent growth, percent decay, doubling time, and half-life
Exponential Formulas
| Growth | y = a(1 + r)^t |
| Decay | y = a(1 - r)^t |
| Doubling time | ln(2) / ln(1 + r) |
| Half-life | ln(0.5) / ln(1 - r) |
Step-by-Step Example
With initial value 100 and a 10% growth rate for 10 periods, use y = 100(1.10)^10. The final value is about 259.37. For decay at 10%, use y = 100(0.90)^10, which gives about 34.87.
Common Uses
- Population growth and decline models.
- Compound growth over repeated time periods.
- Radioactive decay and half-life examples.
- Learning how percentage rates compound over time.
Frequently Asked Questions
What is exponential growth?▼
Exponential growth happens when a quantity increases by a constant percentage rate over equal time intervals.
What is exponential decay?▼
Exponential decay happens when a quantity decreases by a constant percentage rate over equal time intervals.
What is the exponential growth formula?▼
A common formula is y = a(1 + r)^t for growth and y = a(1 - r)^t for decay.
How do doubling time and half-life relate to the curve?▼
Doubling time is the time needed for a growing quantity to double. Half-life is the time needed for a decaying quantity to fall to half its value.
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