Question

The population of a city increased from 40000 in 2000 to 50000 in 2006. Find the continuous growth model rate for the population t years after 2000

Answer 1

continuous growth model = P e^(rt)

$P\cdot e^{rt}$

The population of a city increased from 40000 in 2000 to 50000 in 2006.

so, P = 40,000 and t = 2006 - 2000 = 6

So,

$50,000\text{ = 40,000 }\cdot e^{6r}$$e^{6r}=\text{ 50,000/40,000 = 1.25}$

taking ln for both sides

6r = ln 1.25

r = ln1.25/6 = 0.0372

So, the continuous growth model rate for the population t years after 2000

$40,000e^{0.0372\text{ t}}$