Question 1120673: According to Newton's Law of Cooling, if a body with temperature T1 is placed in surroundings with temperature T0 different from that of T1, the body will either cool or warm to temperature T after t minutes, where T(t)= T0+(T1−T0)e^-kt. A chilled jello salad with temperature 47°F is taken from a refrigerator and placed in a 68°F room. After 5 minutes, the temperature of the salad is 53°F. Use Newton's Law of Cooling to find the salad's temperature after 10 minutes.
I started the problem by doing t(5)=53+(68-53)e^-5k then simplifying it to t(5)=53+(15)e^-5k and now I am stuck on what to do next.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! T(t)= T0+(T1−T0)e^-kt.
T(5)=53=47+21*e^(-5k). To=47. Subtract 47 from both sides then divide both sides by 21
6/21=e^(-5k)
0.286=e^-5k, ln both sides
-1.25=-5k
k=0.25
T(10)=53+21*e^(-10k), or e^-2.5
53+21*e^-2.5=54.72 degrees F.
|
|
|
