Integrated Math 1 / Unit 5: Exponential Functions and Geometric Sequences
5.6 Modeling with Exponential Functions
Notes
To model, find the initial value and the growth or decay factor, then write $y = a \cdot b^t$.
- Compound interest (once a year): $A = P(1 + r)^t$.
- Interpret the parts: $a$ is the starting amount; $b$ tells the percent change per period.
- Example: a town of 12,000 shrinks 2% per year: $P = 12000(0.98)^t$.
- Round only at the end of the calculation.
Practice
A video has 50 views and the number triples each day. Which function models the views after $d$ days?
Start at 50 and multiply by 3 each day.
A town of 12,000 people shrinks 2% each year. About how many people live there after 2 years (nearest whole number)?
$12000(0.98)^2 = 12000(0.9604) = 11{,}524.8$, which rounds to 11,525.
$500 is invested at 4% interest compounded annually. Which expression gives the balance after 3 years?
Each year multiplies by $1.04$, so after 3 years: $500(1.04)^3$.
Ready for more? Take the Unit 5 test.