Approximating Exponential Growth

Exponential growth is given by the formula P=P_oe^rt , where P_o is the initial population, r is the rate of growth as a decimal, t is the time, and P is the population after t units of time. It can be approximated by P=P_o(1+rt).

If the initial population is 100, and the rate of growth is 8%, graph both of the these curves on the same graph for t = 0 to t = 15.

For what values of t does the linear function do a good job of approximating the actual exponential growth?

A quadratic approximation for exponential growth is P = P_o(1 + rt + ½ r² t²).

Now graph the quadratic and the exponential curve on the same graph for t = 0 to t = 15.

For what values of t does the quadratic function do a good job of approximating the actual exponential growth?