Question

a high school decreases by 7% each year. The senior class has 250 students now. How many years will it have about 100 students.
(write an equation, then solve without graphing)
please help

Answer 1

Do you know the formula for exponential decay?

Answer 2

I dont.

Answer 3

Alright no problem. Let's start there. The formula is actually the same for both decay and growth, y = a*b^x. It depends on what you put for those variables to make it grow or decay.

For decay: when a > 0 and b is between 0 and 1, it will be decaying, or decreasing.
For growth: when a > 0 and b is > 1, it will be growing.

So we know we're going to be using the decaying formula here, so y = a(1-r)^x.
a = initial amount = 250.
r = decay rate = 7%;0.07
x = number of time intervals that have passed.
So your formula would be y = 250(.93)^x. Fill in any number for x until you get to 100.

Could you fill in some numbers until you find the closest value to 100 without going under it? I'll give you a hint, 10 < x < 15. So find a number between those values. Here is a good online calculator: http://mathpapa.com/algebra-calculator.html

Don't input the y =, just put what's after the y.