Thanks in advance! Newton\'s law of cooling relates the rate at which a body coo

Question

Thanks in advance!

Newton's law of cooling relates the rate at which a body cools to the difference in temperature between the body and the environment into which it is introduced. The formula is Ft) To Cbt, where Ft) is the temperature of the body at time t, To is the constant temperature of the environment into which the body is introduced, and C and b are constants. Use Newton's law of cooling to solve the problem below. A cup of coffee has cooled from 95 to 60o after 11 minutes in a room at 200. How long will it take to cool to 40o? It will take approximately minutes (Round to the nearest integer as needed.)

Explanation / Answer

F(t) = T0 + Cbt

At t=0, F(t) = 95 , T0 = 20

95 = 20 + C x 1   => C = 75

At t = 11, F(t) = 60 , T0 = 20

60 = 20 + 75.b11

b11 = 40/75 = 0.533

b = 0.533(1/11) = 0.944

now, F(t) = 40, T0 = 20

40 = 20 + 75 . (0.944)t

0.267 = (0.944)t

ln (0.267) = t ln(0.944)

t = ln(0.267)/ ln(0.944)

t = 22.91 min = 23 min

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