Question 327135
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One of two things is going on here.  Either you meant to write "The <i><b>space</b></i> 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 *[tex \Large t] and do the arithmetic.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ F(t)\ =\ 270\ -\ 70\log_5(4t\ +\ 1)]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ F(1)\ =\ 270\ -\ 70\log_5(4(1)\ +\ 1)]


Now for any other value of *[tex \Large t], 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 <i>e</i>.  However for *[tex \Large t\ =\ 1] we need to calculate *[tex \Large \log_5(5)], which can be done in your head.  That's because for any valid base *[tex \Large b], *[tex \Large \log_b(b)\ =\ 1].


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ F(1)\ =\ 200]


On the other hand, if you really meant <i><b>score</b></i>, all bets are off.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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