Math Calculator

Exponential Growth Calculator

Model continuous growth A = A₀ e^{kt} or discrete growth A = A₀(1+r)^t.

Choose a growth model

Enter the initial amount, rate or k, and time.

Model

Initial amount A₀

k (continuous) or r decimal (discrete)

Time t

Clear

About this calculator

How to use Exponential Growth Calculator, plus the formulas and logic behind the results.

Tool description

Continuous compounding uses the natural exponential. Discrete growth compounds once per time unit with relative rate r.

How to use

Select continuous or discrete growth.
Enter A₀, rate k or r, and time t.
For discrete mode enter r as a decimal (5% → 0.05).
Select Calculate to view final amount and growth factor.

Formulas & reference

Continuous: A = A₀ e^{kt}
Discrete: A = A₀ (1 + r)^t
Growth factor = A / A₀

Tips

5% continuous ≈ k = 0.05
Doubling when e^{kt} = 2 → t = ln(2)/k
Discrete r = −0.1 means 10% decline per period
Units of t must match the rate period

Calculation logic

Applies exp(k t) or pow(1+r, t), multiplies by A₀, and reports the growth factor.

r should be decimal (0.05 for 5%), not percent. Negative k or r models decay.