Exponential Growth and Decay Calculator
𝑥 Algebra. Use the Exponential growth and decay formula to find value y, starting value a, rate k, time t: pick the value you want, type the others, and the answer updates as you go.
k > 0 grows, k < 0 decays.
Pick the ○ next to the value you want to find, fill in the others, and it solves as you type.
What each letter means
| Quantity | Unit |
|---|---|
| Value y | no unit |
| Starting value A | no unit |
| Rate k | per unit time |
| Time t | no unit |
Worked example
Find the value y when Starting value A = 1000, Rate k = 0.1 per unit time, Time t = 10.
Using y = A e^(kt): Value y = 2718.3.
Frequently asked questions
What is the formula for Exponential growth and decay?
y = A e^(kt). k > 0 grows, k < 0 decays.
What do the letters stand for, and what units are used?
Value y, Starting value A, Rate k in per unit time, Time t.
How do you calculate value y?
Put the values into y = A e^(kt). For example, with Starting value A = 1000, Rate k = 0.1 per unit time, Time t = 10, value y = 2718.3.
Can I solve for a different value?
Yes. In the calculator above, pick the circle next to any value (value y, starting value a, rate k, time t) and fill in the others: it rearranges the formula for you.
