Suppose the population of a town increased or decreased by t

Suppose the population of a town increased or decreased by the following percentages. For each situation, find the annual percent change of the population. a. Increases by 17% every 6 years Annual percent change: % b. Decreases by 37% every 11 years Annual percent change: % c. Triples in size every 10 years Annual percent change: %

Solution

a. let initial population is 1. and it increased by 17% every 6 years. Therefore after 6 years the population is 1.17

a= b(1+r/100)^t

1.17=1(1 + r/100)^6

1.17^(1/6)=1+r/100

1.17^(1/6) -1=r/100

100(1.17^(1/6) -1)= r

r= 2.65%

c. triples in size every 10 years. Let initially it is 1 then after 10 years it becames 3 times that is 3

we have to use the same formula and on using it we get

100(3^(1/10) - 1)= r

r=11.6%