Definition 4 (Exponential functions). • An exponential function is a function of the form P(t) = Poat, where Po is the initial value of the function and a is the factor by which P changes when t increases by 1. • Writing a = 1+r for some percent change r (as a decimal), we can also express an exponential function as P(t) = Po(1+r)t. • Writing a = ek for some value k (called the continuous growth/decay rate), we can also express an exponential function as P(t) = Poekt. Here e≈ 2.71828 is called the natural base. Example 4. Worldwide wind energy generating capacity, W, was 236,733 megawatts at the end of 2011 and 371,374 megawatts at the end of 2014. Write W as an exponential function of t, the number of years since 2011.

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