Question

Suppose the population of a town is 567 in 2001. The population decreases at a rate of 1.5% every year. What will be the population of the town in 2010?

Answer 1

Exponential decay can be expressed as:

f=ir^t, f=final value, i=initial value, r=common ratio (or rate) and t=times rate is applied (or time).

In this case i=567 and r=(100-1.5)/100=0.985, so the equation is:

p(t)=567(0.985^t), in this case t=year-2001=y-2001 so we can say:

p(y)=567(0.985)^(y-2001) so in the year 2010

p(2010)=567(0.985)^(2010-2001)

p(2010)=567(0.985^9)

p(2010)≈494.89 (to nearest hundredth)

Since we are dealing with people, population needs to be an integer amount

p(2010)≈495 (to nearest whole person :P)