Question

The population of a town in 1999 is 475,000 people. If it is growing at a rate of 3.75% each year. Predict the population (to the nearest whole number) in 2009.

Answer 1

We know that the initial population of a town in 1999 is:

$P_0=475,000_{}_{}$

We also know that it is growing at a rate of 3.75% each year, i.e. at a ratio of r = 0.0375.

We can predict the population in 2009 using the following formula:

$P(t)=P_0\cdot(1+r)^{t-t_0}$

in our problem we have:

P0 = 475,000

r = 0.0375

t0 = 1999

t = 2009

Replacing these values in the formula above we get:

$\begin{gathered} P(2009)=475,000\cdot(1+0.0375)^{2009-1999} \\ P(2009)=475,000\cdot(1.0375)^{10} \\ P(2009)=686395.8727 \end{gathered}$

Answer

By 2009 the population will be 686,396 to the nearest whole number.