# Math Help - Temperature Equation: Please!?!

I am so stuck on this problem, my brainiac sister cant even solve it... Please help if your a Math Wizz.. lol Thank u so much !

Given: T = R + (T0 – R) e kt , where T is temperature,
T0 is initial temperature, R is room
temperature, t is time in minutes, and k is
a constant you have to calculate.

If the room is 35° F and a boiling cup of water
is 212° F at t = 0 (9:00 AM) and after
t = 20 minutes the temperature is 160° F.
Calculate k for the cup and use the above equation
to predict the temperature at 11:00 AM. This method is used in forensics.

2. Hi,
Originally Posted by AFan
If the room is 35°F and a boiling cup of water is 212° F at t = 0 (9:00 AM)
Using the formula we are given, this can be written $212 = 35 +(T_0-35)\exp(k\times 0)$. This equation can be solved for $T_0.$
and after t = 20 minutes the temperature is 160° F.
Again, using the formula we get $160 = 35+(T_0-35)\exp(k\times 20)$. As we know the value of $T_0$, this equation can be solved for $k$.