Question

The population p of a small town, in thousands, is given by p=7⋅1.08t where t is time measured in years. Use a calculator or computer to estimate the derivative p′(8).

Answer 1

To estimate the derivative p′(8) of the function p=7·1.08t, differentiate the exponential function and evaluate it at t=8.

Step-by-step explanation:

The question asks for an estimation of the derivative p′(8) for the function p=7·1.08t, where p is the population of a small town in thousands and t is time measured in years. To find the derivative at t=8, we use the mathematical definition of a derivative or apply differentiation rules to the exponential function. Given that p=7·1.08t, we apply the exponential differentiation rule to get p′(t) = 7·ln(1.08)·1.08t. After calculating, we substitute t=8 into p′(t) to estimate p′(8).