ACT Math

Exponential growth and decay on ACT Math

October 6, 2026 · 5 min read

Exponential growth and decay look like y = a(1 ± r)^t, or y = ab^t. Growth multiplies by more than 1. Decay multiplies by a number between 0 and 1. Sequences that multiply by a constant are the discrete version, in geometric sequences.

Read a, b, and t

a is the start. b is the multiplier per time unit. t is how many times you multiply. Percent change is the r in (1 + r), in percent change. Compound interest is the money version, in compound interest.

Exponent rules for simplifying b^t are in exponent rules.

The bottom line

Start times multiplier to the time. Multiplier bigger than 1 grows. Between 0 and 1 decays.

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