SAT Math: Exponential Growth and Decay
33+ practice questions in Praczo
The concept, explained
- 1
Exponential growth: f(t) = a(1 + r)^t. Decay: f(t) = a(1 − r)^t. Here a is the initial amount, r is the rate as a decimal, and t is time.
- 2
The base of the exponential tells you the growth factor per unit of time. Base 1.05 → 5% growth per period. Base 0.80 → 20% decay per period.
- 3
To find the rate from a base: subtract 1 (for growth) or subtract from 1 (for decay). If base = 1.12, growth rate = 12%.
- 4
Doubling/halving problems use base 2 or ½ with an adjusted exponent: "doubles every 4 years" → f(t) = a · 2^(t/4).
- 5
Exponential ≠ linear. Exponential applies the same percentage each period; linear adds the same fixed amount each period.
- ✗ Misreading the growth rate: if base = 1.12, the rate is 12%, not 1.12 and not 112%.
- ✗ Adding percent changes linearly: 10% growth per year for 3 years is not 30% total — it's 1.1³ − 1 ≈ 33.1%.
SAT-style practice
A bacterial population is modeled by P = 200(1.15)^t, where t is measured in hours. Which statement best describes this model?
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