Model continuous growth or decay with P(t) = P0 * e^(rt) and live validation.
Last updated: June 2026 | By Patchworkr Team
Exponential models change by a constant percentage each period. That is why they are used for population growth, radioactive decay, and continuous compounding.
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.
Example: 1000 * e^(0.05 * 10) = 1648.72.
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
Yes. If the rate is zero, the value stays constant and there is no doubling time or half-life.
Decay means the quantity shrinks over time, so the model uses a negative signed rate.
Yes. The formula works for any real-valued time period as long as the inputs are finite.
Invalid input is rejected instead of being silently converted into zero.
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