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 = abx, 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.