An aluminium beam was brought from the outside cold into a machine shop where the temperature was held at 65 F. After 10 min, the beam warmed to 35 F, and after another 10 min its temperature was 50 F. Use Newton's Law of Cooling to estimate the beam's initial temperature.
The formula is:
$$\ T - T_s = (T_0 - T_s)e^{-kt}$$
$$\ T_0 = 65~~~T_s = 35~~~~T = 50~~~~k = ?$$
I'm supposed to solve for t, but I don't see what k is supposed to be..

Question

An aluminium beam was brought from the outside cold into a machine shop where the temperature was held at 65 F. After 10 min, the beam warmed to 35 F, and after another 10 min its temperature was 50 F. Use Newton's Law of Cooling to estimate the beam's initial temperature.
The formula is:
$$\ T - T_s = (T_0 - T_s)e^{-kt}$$
$$\ T_0  = 65~~~T_s = 35~~~~T = 50~~~~k = ?$$
I'm supposed to solve for t, but I don't see what k is supposed to be..

shamil98 · Answer

@mathmale

shamil98 · Answer

I think I set the values wrong.

mathmale · Answer

@shamil98  :   Very sorry about that abuse; I have taken care of it.
To find that k value, you need to solve the differential equation first, and then substitute the given values of the variables (called "initial conditions") into your solution to determine k.
Have you done this sort of thing before, with easier differential equations?

shamil98 · Answer

Yes, we're studying differential equations right now.

shamil98 · Answer

How would I set up the differential equation for this?..

loser66 · Answer

http://www.ugrad.math.ubc.ca/coursedoc/math100/notes/diffeqs/cool.html

anonymous · Answer

maybe @***[ISURU]*** 
can help u