For each counties in the metro area, it gives an estimate of thepopulation on Jan. 1, 2000, and the percent change between 1/1/2000and 1/1/2010. If we assume that the percent change for each countyis constant, then the population of each county can be modeledusing an exponential function with a growth rate given by theannual percentage change.
County | 2000 Population Estimate | Annual Percent Change (Growth Rate) |
Cherokee | 141,925 | 4.2% dP/dt=0.042P |
Fayette | 91,263 | 1.6% dP/dt=0.016P |
- Find an exponential function of the formP(t)=P0ekt , which gives the population ofthe county in the year 2000 + t.
- Evaluate the function at t = 16 and give a verbalinterpretation of your answer.
- Find the derivative of the function.
- Evaluate the derivative at t = 16 and give a verbalinterpretation of your answer.
