Question 327135: Hi, I'm having trouble solving this problem and I can sure use a little help. I would really appreaciate it. Here is the problem. "The score in a landfill decreases with time as given by the function F(t)= 270 - 70 log5 (4t + 1),where t is measured in years. How much space is left when t = 1? Thanks! Found 2 solutions by stanbon, solver91311:Answer by stanbon(57309) (Show Source):
You can put this solution on YOUR website! F(t)= 270 - 70 log5 (4t + 1),where t is measured in years. How much space is left when t = 1?
F(1) = 270 - 70*log5(4+1)
F(1) = 270 - 70*log5(5)
Note: log5(5) is 1 because 5^1 = 5.
F(1) = 270-70
F(1) = 200
One of two things is going on here. Either you meant to write "The space in a landfill decreases with time..." or you are going to have to explain the relationship between score and space remaining in order for someone to help you. If it is the former case, just plug in a 1 everywhere you see a and do the arithmetic.
Now for any other value of , this could be some tricky arithmetic because you would probably have to use the base conversion formula to get the base 5 log of something -- unless you were using Excel or some other calculation system that can calculate the log of something other than base 10 or base e. However for we need to calculate , which can be done in your head. That's because for any valid base , .
On the other hand, if you really meant score, all bets are off.