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?

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)