Question

As a town gets​ smaller, the population of its high school decreases by 4% each year. The senior class has 320 students now. In how many years will it have about 100 ​students? Write an equation. Then solve the equation without graphing.

Write an equation to represent this situation. Let n be the number of years before the class will have 100 students.

Answer 1

• c(n) = 320·0.96^n
• 28 years

Explanation:

Each year, the class size is multiplied by 1 - 4% = 96% = 0.96. After n years, it has been multiplied by that number n times. Repeated multiplication is signified using an exponent.

Class size (c) can be modeled by ...

c(n) = 320·0.96^n

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You want to find n such that c(n) = 100. Put in that value and solve.

100 = 320·0.96^n

100/320 = 0.96^n . . . . . . . divide by 320

log(100/320) = n·log(0.96) . . . . . . . take logs

log(100/320)/log(0.96) = n ≈ 28.4932

In about 28 years, the class will have 100 students.