As a town gets smaller, the populaion of its high school decreases by 4% each year. The senior class has 250 students now. In how many years will it have 100 students?

Answer 1

At the end of each year, the population drops to 0.96 times the level at the start of the year, so the exponential decay function is

P(t) = P₀ (0.96)^t

P₀ = initial population (at time t = 0)

t = years elapsed since P was P₀

P(t) = 250 (0.96)^t

T = time to drop to 100

100 = 250 (0.96)^T

log(100/250) = T log(0.96)

T = log(100/250) / log(0.96) = 22.45 years

Test the answer. You can choose any base for the logs, as long as it is the same for all the logs.