Question

The population of a small town is 47,288 and has been continuously declining at a rate of 2.4% each year. What is the approximate population of the town in 21 years?

Answer 1

Use decay formula
F=P(1-i)^n
F=future value
P=present value
i=decay rate (0.024)
n=number of years.

Answer 2

Without passing judgment on mathmate's approach, I'd like to suggest another:\[y=y _{0}e ^{kt}\] is the standard growth model (which can be adapted to decay).

If the current population is 47288, at time t = 0, then \[y _{0}=47288.\] After the first year, t = 1 and the population is 0.024(47288) less. The only unknown quantity is then k.

Find this k.

Then \[y=47288e ^{k(1)}\]

After substituting your value of k in the above equation, let t= 21 (years) to obtain the approx. population of the town at that time.