Exponential Growth & Decay

A quantity that changes by a constant percent follows y = a(1 ± r)ᵗ.

Start with the initial amount a, and the growth factor 1 + r or the decay factor 1 − r.
Growth by 5% per year multiplies by 1.05 each year.
Compound interest: A = P(1 + r/n)^(nt).
Use trial values or logs to find a time.

Watch out: Adding the percent each time instead of multiplying.

Worked example

$1,000 grows 10% per year. What is it worth after 2 years?

Answer: $1,210

Try it yourself

Practice questions for this skill are for signed-in students. A free account is all you need.