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)