SOLUTION: please help me solve this problem it is a logarithmic, I think. As a town gets smaller, the population of its high school decreases by 12% each year. the student body numbers 125 s

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: please help me solve this problem it is a logarithmic, I think. As a town gets smaller, the population of its high school decreases by 12% each year. the student body numbers 125 s      Log On


   

Question 750242: please help me solve this problem it is a logarithmic, I think. As a town gets smaller, the population of its high school decreases by 12% each year. the student body numbers 125 students now. in how many years will it number about 75 students?
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Simplest way to analyze it is that each year population is pop*(1.00-0.12).

Starting with 125 students,
1 year 125*(1-0.12)
2 year 125%2A%281-0.12%29%5E2
3 year 125%2A%281-0.12%29%5E3
n year highlight%28125%2A%281-0.12%29%5En=125%2A%280.88%29%5En%29

You are looking for how 75=125%280.88%29%5En
then
highlight%280.6=%280.88%29%5En%29

Can you take this the rest of the way to the solution for n? Take logarithms of both sides, and use the rule about logs, log%28%28b%5Ea%29%29=a%2Alog%28%28b%29%29