Problema Solution
The function p(t)=10,000e^0.075 estimates the population of a city at time t years after 1980
Estimate the year the population doubled its 1980 population
Answer provided by our tutors
The initial population was 10,000 (at t = 0, p(0) = 10,000e^0 = 10,000*1 = 10,000)
Thus, we need to find t such that p(t) = 20,000
So, 20,000 = 10,000e^(0.075t)
20,000/10,000 = 2 = e^(0.075t)
Take the natural log of both sides: ln 2 = ln(e^0.075t) = 0.075t
Thus, t = (ln 2)/0.075 = 9.24 years
So, the population doubles by 1989. (1980 + 9.24)