Integrated Math 1 / Unit 5: Exponential Functions and Geometric Sequences
5.2 Exponential Growth
Notes
In exponential growth the factor $b > 1$. A growth rate $r$ gives $b = 1 + r$, so growth of 10% means $b = 1.1$.
- Model: $y = a(1 + r)^t$.
- Doubling means $b = 2$; tripling means $b = 3$.
- Example: $1,000 growing 5% per year for 2 years: $1000(1.05)^2 = 1102.50$.
- Convert percent to a decimal before adding to 1.
Practice
A population of 200 grows 10% per year. Which function models it after $t$ years?
A 10% increase multiplies by $1 + 0.10 = 1.1$ each year.
An account of $1,000 grows 5% per year. What is the balance after 2 years?
$1000(1.05)^2 = 1000(1.1025) = 1102.50$. Note $1,100 would be simple (linear) growth.
A culture starts with 3 cells and doubles every hour. How many cells are there after 5 hours?
$3 \cdot 2^5 = 3 \cdot 32 = 96$.
Ready for more? Take the Unit 5 test.