Question

The rate of change of the population of a small town is dP/dt=kP

Where P is the population, t is the time in years and k is the growth rate.

If P=20000 when t=3 and P=30000 when t=5, what is the population when t=10?

Round your answer to the nearest integer.

Answer 1

Oh, well, when the rate is proportional to the amount, we have an e^kx kind of a thing

P = Pi e^kt

at t = 3
20,000 = Pi e^3k

at t = 5
30,000 = Pi e^5t

so

3/2 = e^5k/e^3k = e^2k

so
ln (1.5) = 2 k

got it?