C is the difference between the the initial temperature and room temperature. C is NOT 180.
Your first equation is wrong because, as I said, C is NOT "the initial temperature".So I basically need to find S. My attempt is basically solving a system of equations, and I really doubt this is how to do it because my answers have been completely wrong.
I need ALOT of help in this problem. All I have so far is filling in the values for everything but S and k in the equations, and I do not have the necessary math skills to solve the system of equations to find what k and S are.
Plug this into the other equation:
At t= 0, T= 180 so 180- S= C.
At t= 1, T= 180- 8= 172 so .
At t= 2, T= 172- 26= 146 so .
Those are the three equations you need to solve for S, C, and k.
One thing you can do, of course, is to replace "C" in the last two equations by 180- S:
Seeing "k" and "2k" in the exponent, I would try squaring both sides of the first equation:
And since that and are equal to you can set them equal to get a single equation for S.