Question 1099829: Newton's Law of Cooling governs the temperature of an object T(t)T(t) initially at temperature T0T0 as a function of time when placed in an environment with temperature TeTe . The object's temperature is given by the equation T(t)=Te+(T0−Te)e−rtT(t)=Te+(T0−Te)e−rt where rr is the cooling rate of the system.
A dish of lasagna is backed at 375F and placed on the counter of the kitchen at room temperature (68F). After 6 minutes, the lasagna cooled to 318F. What will its temperature be 9 minutes later (15 minutes after it was removed from the oven)? Round your answer to one decimal place.
By the way this is a similar question to the one I posted yesterday, but there is one additional number so it's a little bit harder.
Answer by jorel1380(3719)   (Show Source):
You can put this solution on YOUR website! Given the circumstances of this problem, we have:
318=68+(375-68)*e^-rt, or 250=307e^-rt or
0.8143322475570032573289902280130=e^-6r
ln 0.81433224755700325732899022801303=ln e^-6r=-6r ln e=-6r
r=0.03423113828749178672982540769096
So, for T(15), we have:
T(15)=68+307*e^-15*0.03423113828749178672982540769096
=68+183.714
=251.714
The temperature after 15 minutes will be approximately 251.714 deg. F
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