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For each counties in the metro area, it gives an estimate of the population on Jan....

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Advance Math

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

  1. Find an exponential function of the formP(t)=P0ekt , which gives the population ofthe county in the year 2000 + t.
  2. Evaluate the function at t = 16 and give a verbalinterpretation of your answer.
  3. Find the derivative of the function.
  4. Evaluate the derivative at t = 16 and give a verbalinterpretation of your answer.

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