Exponential growth and decay calculator: model populations, investments
An exponential growth and decay calculator computes future values using continuous (e^rt) or compound ((1+r)^t) formulas. It also finds doubling time for growth and half-life for decay.
Growth and decay formulas
Continuous model: A = P·e^(rt) for growth, A = P·e^(−rt) for decay. Compound model: A = P·(1+r)^t for growth, A = P·(1−r)^t for decay.
Doubling time is ln(2)/r and half-life is also ln(2)/r, regardless of which model is used.
A = P · e^(rt)
Continuous exponential growth. This is the specific relationship the calculator applies when building the result.
t₂ = ln(2) / r
Doubling time (or half-life). This is the specific relationship the calculator applies when building the result.
Worked example and interpretation
A worked example helps translate the exponential growth and decay calculator maths into a realistic scenario so the user can compare the headline result with a concrete set of inputs.
That matters because a result is easier to trust when the page shows how the same logic behaves in a practical case instead of leaving the formula abstract.
Using the result well
Use the exponential growth and decay calculator output as a planning aid, then compare it with the assumptions, units, and caveats shown elsewhere on the page before acting on the number alone.
That extra interpretation step matters because a calculator can simplify the arithmetic but still cannot replace real-world context such as local rules, contract terms, or individual circumstances.
Frequently asked questions
When should I use continuous vs compound?
Use continuous when growth happens constantly (like bacteria or radioactive decay). Use compound when growth occurs at discrete intervals (like annual interest).
What is the difference between doubling time and half-life?
They use the same formula — ln(2)/r — but doubling time applies to growth while half-life applies to decay.
How can I check the exponential growth and decay calculator: model populations, investments, and radioactive decay result manually?
The safest manual check is to follow the same formula or rule one step at a time and compare that working with the calculator output. That catches sign errors, bracket mistakes, and input-order mixups without requiring any extra method beyond the underlying maths itself.
