Exponential Growth and Decay Simulator

Visualize percent growth, percent decay, doubling time, and half-life

Initial value

Rate (%)

Time t

Mode

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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