As a town gets​ smaller, the population of its high school decreases by 5​% each year. The senior class has 160 students now. In how many years will it have about 100 ​students? Write an equation.

Answer 1

A decrease of 5% means that the population each year is 95% of the year before.

160(0.95) = 152 next year

152(0.95) is also 160(0.95)(0.95), right? Both come up with the same solution. Of course, we'd say 160(0.95)².

So, if n = the number of years from now...

100 = 160(0.95)ⁿ