Question

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. Then solve the equation without graphing. Write an equation to represent the situation. Let n be the number of years before the class will have 100 students.

Answer 1

T_n = 160(0.05)^(n - 1)

At T_n = 100, n = 1 year

Explanation:

We will use geometric progression to solve this question.

Formula for nth term of a GP is;

T_n = ar^(n - 1)

We are told the population of its high school decreases by 5% each year.

This means r = 0.05

senior class has 160 students. Thus a = 160

Thus,T_n = 160(0.05)^(n - 1)

Where n is number of years after now.

We want to find the number of years before the class will have 100 students

Thus;

160(0.05)^(n - 1) = 100

(0.05)^(n - 1) = 100/160

(n-1)In 0.05 = In (100/160)

-2.9957(n - 1) = -0.47

(n - 1) = 0.47/2.9957

n = 1 + 0.1569

n = 1.1569

Approximating to the nearest whole number gives n = 1