# Common Core Standards: Math

#### The Standards

# High School: Functions

### Interpreting Functions F-IF.8b

**b. Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)^{t}, y = (0.97)^{t}, y = (1.01)^{12t}, y = (1.2)^{t⁄10} and classify them as representing exponential growth or decay.**

If we have a function of the form *y* = *ab*^{x}, we can either be describing exponential growth or exponential decay. If *a* > 0 and 0 < *b* < 1, the equation represents **decay**. If *a* > 0 and *b* > 1, the equation represents **growth**.

Equations like *y* = *a*(1 + *c*)^{x} can represent the balance of a savings account after *x* years with starting balance *a* and interest rate *c*. If the annual interest rate is 2% and we start with $100, how much money will we have in 10 years? Just substitute in our values, and we're good to go.

*y* = *a*(1 + *c*)^{x} = 100(1 + 0.02)^{10} = $121.90

Not too bad, but don't go spending it all on bubble gum. We may want to save up for a new iPod. Or to pay for Coach Gibson's medical bills.