
Newton's Law of Cooling
Hi everyone, thanks for taking the time to help me out!
Question: An object of temperature 120 degree F is placed in a medium maintained at a constant temperature m degree F. At the end of 2 minutes the temperature of the object is 90 degree F and after another 2 minutes its temperature is 72 degree F.
(i) Find m
(ii) When will the temperature of the object be 61.20 degree F?
(iii) What is the temperature of the object at the end of 8 minutes?
(i) T(t)=Ta+(ToTa)e^kt
I know that Ta=90 F, To can be 120 degree F when T(2)=90 and t=2. I still have two unknowns left and i cant solve for Ta, so i need help here.
T(2)=90=Ta+(12090)e^2t
As for the rest if i can get the equation i will be able to solve!

At T(0)=120.
By $\displaystyle \frac{dt}{Tm}=kdt$
Integrate both sides gives:
$\displaystyle ln(Tm)=kt+C$
$\displaystyle T=e^{kt+C}+m$
$\displaystyle T=Ke^{kt}+m$
At T(0) we have T=120
$\displaystyle 120=Ke^{kt}+m$......[1]
At T(2) we have 90:
$\displaystyle 90=Ke^{2k}+m$....[2]
At T(4) we have 72:
$\displaystyle 72=Ke^{kt}+m$....[3]
We have three equations to solve, [1], [2], and [3].
From [1], K=120m
Sub into [2] and get
$\displaystyle 90=(120m)e^{2k}+m$
Can you finish?.

I'm not exactly sure where to go from here after ive substituted into the equation. I still have m and k left.