Algebra 1 / Unit 7: Exponents and Exponential Functions
7.5 Exponential Growth and Decay
Notes
- Growth: $y = a(1 + r)^t$, where $r$ is the percent increase per time period.
- Decay: $y = a(1 - r)^t$, where $r$ is the percent decrease.
- A growth of $8\%$ gives factor 1.08; a decay of $8\%$ gives factor 0.92.
- Compound interest is exponential growth: $1,000 at $5\%$ per year grows to $1000(1.05)^t$.
Practice
A town of 4,000 people grows $3\%$ per year. Which models the population after $t$ years?
Growth factor $1 + 0.03$.
A car worth $20,000 loses $15\%$ of its value each year. Its value after 2 years:
$20000(0.85)^2 = 14450$.
$y = 50(0.9)^t$ shows:
The factor 0.9 means losing $10\%$ each period.
Ready for more? Take the Unit 7 test.