SOLUTION: A frozen turkey is placed in an oven preheated to a temperature of 425 degrees F. The temperature of the inside of the turkey after t minutes is given by M(t)=425(1-e^-kt), where k

Question 62067: A frozen turkey is placed in an oven preheated to a temperature of 425 degrees F. The temperature of the inside of the turkey after t minutes is given by M(t)=425(1-e^-kt), where k is a constant. The value of k is 0.047. How long will it take the inside of the turkey to reach a temperature of 400 degrees?
Found 2 solutions by stanbon, Nate:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A frozen turkey is placed in an oven preheated to a temperature of 425 degrees F. The temperature of the inside of the turkey after t minutes is given by M(t)=425(1-e^-kt), where k is a constant. The value of k is 0.047. How long will it take the inside of the turkey to reach a temperature of 400 degrees?
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M(t)=425(1-e^-kt), and k=0.047
400=425(1-e^(-0.047t))
0.941176... = (1-e^(-0.047t))
1-0.941176... = e^(-0.047t)
1-0.941176... = e^(-0.047t)
0.058835...=e^(-0.047t)
Take the natural log of both sides to get:
-2.83321...=-0.047t
t=60.28 minutes
Cheers,
Stan H.

Answer by Nate(3500) (Show Source): You can put this solution on YOUR website!
400 = 425(1 - e^(-0.047*t))
16/19 = 1 - e^(-0.047t)
-3/19 = - e^(-0.047t)
3/19 = e^(-0.047t)
ln(3/19) = -0.047t
ln(3/19)/-0.047 = t
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