Exponential Growth & Decay

Growth formula: y = a(1 + r)^t

Decay formula: y = a(1 - r)^t

a = initial value, r = rate (as decimal), t = time

Growth example: Population of 5,000 grows 3% per year: y = 5000(1.03)^t

Decay example: Car worth $20,000 loses 15% per year: y = 20000(0.85)^t

SAT question patterns:

"What does the 1.03 represent?" — 3% annual growth

"What does the 5000 represent?" — initial population

"What is the value after 5 years?" — plug in t = 5

Key distinction: Linear = constant AMOUNT added each time. Exponential = constant PERCENTAGE multiplied each time. The SAT tests whether you know the difference.

Reference:

Wikipedia: Exponential Growth

https://en.wikipedia.org/wiki/Exponential_growth