Question

As a town gets​ smaller, the population of its high school decreases by 8​% each year. The senior class has 250 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

Answer:

11 years

Step-by-step explanation:

This is a case of exponential decay.

Let n = number of years; p = population after n years; a = initial population; r = rate of decay

p = a(1 - r)^n

Now we substitute the numbers we know leaving n as the only unknown.

100 = 250(1 - 0.08)^n

100 = 250(0.92)^n

Divide both sides by 250.

0.4 = 0.92^n

Take the log base ten of each side.

log 0.4 = log 0.92^n

Use log rule: log a^n = n * log a

log 0.4 = n * log 0.92

Divide both sides by log 0.92

$\dfrac{\log 0.4}{\log 0.92} = n$

n = 10.989

Answer: 11 years