Question

For each counties in the metro area, it gives an estimate of the population on Jan. 1, 2000, and the percent change between 1/1/2000 and 1/1/2010. If we assume that the percent change for each county is constant, then the population of each county can be modeled using an exponential function with a growth rate given by the annual 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 form P(t)=P₀e^kt , which gives the population of the county in the year 2000 + t.
2. Evaluate the function at t = 16 and give a verbal interpretation of your answer.
3. Find the derivative of the function.
4. Evaluate the derivative at t = 16 and give a verbal interpretation of your answer.

Answer 1

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