SOLUTION: I wasn't sure what "type" of problem to put this under so hopefully you can help me. Question: Suppose that a 50 million gallon contamination is reduced by 20% every year. How

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: I wasn't sure what "type" of problem to put this under so hopefully you can help me. Question: Suppose that a 50 million gallon contamination is reduced by 20% every year. How       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 322700: I wasn't sure what "type" of problem to put this under so hopefully you can help me.
Question: Suppose that a 50 million gallon contamination is reduced by 20% every year. How long will it take to have only 100,000 gallons of oil contamination left in the Gulf? I am not sure how to figure this out.
Thank you for your help
Beth
Answer by galactus(183) About Me  (Show Source):
You can put this solution on YOUR website!
Since it is decreasng by 20%, then 80% or 4/5 remains and we can write
50%284%2F5%29%5Et, where t is the year.
So we do not have such large numbers to deal with, divide by a million and let the initial amount be 50 and then 100000 would be 1/10.
Now, set this equal to 1/10 and solve for t.
50%284%2F5%29%5Et=1%2F10
%284%2F5%29%5Et=1%2F500
tln%284%2F5%29=ln%281%2F500%29
t=ln%281%2F500%29%2Fln%284%2F5%29
t=27.85 years