The populations P (in thousands) of a particular county from 1971 through 2014 can be modeled by P = 79.9e0.0317t. Where t represents the year, with t = 1 corresponding to 1971.

Question

a) Use the model to complete the table. (Round your answers to the nearest whole number.)

Year	Population
1980
1990
2000
2010

(b) According to the model, when will the population of the county reach 340,000?

Answer 1

The table can be filled out by using the calculator to solve for the P using the equation, get t by subtracting 1970 from the year.

Part b can be solved by putting setting P= 340 and dividing through by 79.9 so that the exponential term is isolated. Then take natural log (ln) of both sides of the equation. This gives:

ln(340/79.9) = 0.0317 t

divide by 0.0317 to solve for t: t = [ln (340/79.9)] / 0.0317 = 45.7

Since this is the number of year since 1970, add 1970+45.7 = 2015.7 So the population would reach 340 thousand sometime around 2015 and 2016, assuming the model is correct.