Question

The population of a small town can be described by the equation PN equals 4000×1.04 to the nth power. Where n is the number of years after 2005. Explain in words what this equation tells us about how the population is changing.

Answer 1

"the population of the small town is growing at a rate of 4% per year (years after 2005)."

Explanation:

The basic equation is:

`F=P(1+r)^t`

Where

F is the future amount

P is the present amount

r is the rate of growth per year (if negative, then rate of decline)

t is the time in years

From the equation given:

`P_N=4000*1.04^n`

We can write 1.04 as (1+0.04) so when comparing with the formula we see that r = 0.04, that is 4%. Thus, we can say the population of the small town is growing at a rate of 4% per year (years after 2005).