Thread: Newton's law of Cooling word problem.

Hello everyone! I am new here and I am in my first year of calculus in college. I am having trouble on a pretty difficult question that I have spent hours trying to understand, but I just can’t get it. I have asked several tutors and they can’t figure it out! So I am hoping you guys can help me get an answer here or at least some direction. I am getting really frustrated!
The question is:
A potato is put into a hot oven, maintained at a constant temperature of 200 degrees C. Suppose that at time t=30 minutes, the temperature of the potato is 120 degrees C and is increasing at a constant rate of 2 degrees C/minute. Newton’s Law of Cooling (or in this case, warming) implies that the temperature of the potato at the time t will be given by the following function:
T(t):200 - ae^(-bt)
(ae is raised to the -bt power)
Find a and b.
HELP :[

Whynot substitute to points into the equation,

for (t,T) = (30, 120) & given the increase is 2 degrees per minute (30+1, 120+2), two equations, to solve two unknowns.

Originally Posted by pickslides

Whynot substitute to points into the equation,

for (t,T) = (30, 120) & given the increase is 2 degrees per minute (30+1, 120+2), two equations, to solve two unknowns.

Except that is only approximate, it gives ~1% error in both a and b.

(The error could have been made smaller by using 30+0.0001 and 120+0.0002 rather than +1 and 2 used in your post)

CB

Thanks guys, I finally was able to solve it!