Exponential Growth Calculator

Exponential Growth Calculator

Model continuous growth or decay with P(t) = P0 * e^(rt) and live validation.

Last updated: June 2026 | By Patchworkr Team

Growth and Decay
Enter a positive starting value, a non-negative rate, and the number of periods. The mode determines whether the rate is applied as growth or as decay.
Result
Formula
P(t) = 1,000 * e^(0.050000 * 10)
Final value
1,648.7212707
Change
648.7212707
Percent change
64.87212707%
Doubling time: 13.8629

What the model means

Exponential models change by a constant percentage each period. That is why they are used for population growth, radioactive decay, and continuous compounding.

Doubling and half-life

The time constant depends only on the rate, not the starting value. For growth it is the doubling time. For decay it is the half-life.

Formula and example

P(t) = P0 * e^(rt)

Example: 1000 * e^(0.05 * 10) = 1648.72.

Worked Example

Calculate decay for 800 with a 12% rate over 6 periods.

1. Set P0 = 800, r = 0.12, and t = 6.

2. Use decay mode, so the signed rate is -0.12.

3. Compute 800 * e^(-0.12 * 6) = 454.64.

Final answer: 454.64

Frequently Asked Questions

Can the rate be zero?

Yes. If the rate is zero, the value stays constant and there is no doubling time or half-life.

Why does decay use a negative exponent?

Decay means the quantity shrinks over time, so the model uses a negative signed rate.

Can time be fractional?

Yes. The formula works for any real-valued time period as long as the inputs are finite.

What if I enter an invalid value?

Invalid input is rejected instead of being silently converted into zero.

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