Bob loves vegetarian pizza. How long will it take Bob's pizza to cool to 110 degrees if he bakes it at 450 degrees for 20 minutes? The temperature in his house is a balmy 70 degrees.
T(t) = Ts + Do*e^(-k*t) where...
Do = initial temperature difference (Initial Temperature - Ts)
Ts = surrounding temperature
t = time
k = constant (cooling rate)
The Attempt at a Solution
We know the following...
> Ts := 70;
The initial temperature difference (Do) is the pizza temperature (when it came out of the oven) minus the surrounding temperature...
> Ti := 450;
> Do := Ti-Ts; ** 450 - 70 = 380 degrees **
We also know the temperature at time "t"... 110 degrees.
> T := 110;
Therefore our formula is now:
110 = 70 + 380 exp(-k*t)
** The problem is that I need to know what the cooling constant "k" is, in order to solve for the real question, "t". **
The 20 minutes given in the problem must be useful, but I'm not sure how. Can you please help?