Question

The rate of growth of a town's population is given by the differential equation: dp/dt = kp, where p is the population in t years after a census was taken in 1986. When the census was taken the population of the town was 10,000 and in 1996 it was 15,000. What is the population expected to be in the year 2006?

Answer 1

Again, use y=Ce^kt and plug and chug.

Answer 2

1) rearrange: dp/p = kdt
2) integrate both sides: ln(p) =kt + c
3) plug in your two values for t and p to solve for k and c
4) substitute k and c and multiply both sides by e: p=e^(kt+c)
5) plug in 2006 to get your answer.