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.

Step-by-step 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.

step-by-step explanation:

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