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 25 % every 6 years annual percent change % b. Decreases by 22 % every 8 years annual percent change % c. Triples in size every 12 years annual percent change % d. Increases by 44 % every 10 years annual percent change %

Solution

a) x⁶ = 1.25 => x = 1.0378908

annual percentage change = 3.78908%

b) x⁸ = 0.78 => x = 0.969419665

   annual percentage change = -3.0580335%

c) x¹² = 3 => x = 1.095872691

   annual percentage change = 9.5872691%

d) x¹⁰ = 1.44 => x = 1.037137289

   annual percentage change = 3.7137289%