AP Precalculus / Unit 2: Exponential and Logarithmic Functions
2.5 Exponential Function Context and Data Modeling
Notes
Growth by $r$% per period: $f(t)=a(1+r)^t$. Decay: $a(1-r)^t$.
- Continuous growth: $ae^{kt}$.
- Fit exponential regression when data have roughly constant ratios.
Practice
A town of 2,000 grows 3% per year. A model:
Growth factor $1+0.03$.
A car loses 15% of its value each year. The decay factor:
$1-0.15$.
In $f(t)=500(1.08)^t$, 500 represents:
The value at $t=0$.
Ready for more? Take the Unit 2 test.