SAT and ACT math terms · SAT Math, ACT Math
Exponential growth and decay
Exponential growth and decay: Change by a constant percentage or factor per time period, modeled by y = a(1 + r)ᵗ for growth or y = a(1 − r)ᵗ for decay.
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What it means
In an exponential model, a is the initial value, and the base (1 + r) or (1 − r) is the growth or decay factor. Linear change adds a constant amount. Exponential change multiplies by a constant factor, so it accelerates over time.
In a table with evenly spaced inputs, exponential data has a constant ratio between consecutive outputs.
Example
A town of 20,000 grows 3% per year: P = 20,000(1.03)ᵗ. A car worth $30,000 loses 15% per year: V = 30,000(0.85)ᵗ.
On the exam
Expect to identify the growth rate from an equation, choose between linear and exponential models, and interpret constants.