Question 1096964
According to Newton's law of cooling, the temperature T(t)=T(a)+((T(0)-T(a))e^-kt; where T(t) is the temperature after time t;T(0) is the initial temperature, T(a) is the ambient temperature of the surrounding environment, and k is the cooling constant. So, here we have:
T(2)=182=69+(204-69)e^-2k
Then:
113=135e^-2k
0.83703703703703703703703703703704=e^-2k
ln 0.83703703703703703703703703703704=ln e^-2k=-2k ln e=-2k
k=0.08894347986304444010218177518887
So, in order to reach 106 degrees, we have:
106=69+(204-106)e^-0.08894347986304444010218177518887t
0.37755102040816326530612244897959=e^-0.08894347986304444010218177518887t
ln 0.37755102040816326530612244897959=ln e^-0.08894347986304444010218177518887t=-0.08894347986304444010218177518887t ln e=-0.08894347986304444010218177518887t
t=10.9513 minutes
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