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.

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

n = 10.989

11 years

do have an equation or graph or

step-by-step explanation: