(1 point) Newton\'s law of cooling states that the temperature of an object chan

Question

(1 point) Newton's law of cooling states that the temperature of an object changes at a rate proportional to the difference between its temperature and that of its surroundings. Suppose that the temperature of a cup of coffee obeys Newton's law of cooling. If the coffee has a temperature of 195 degrees Fahrenheit when freshly poured, and 2 minutes later has cooled to 184 degrees in a room at 66 degrees, determine when the coffee reaches a temperature of 144 degrees. The coffee will reach a temperature of 144 degrees in minutes

Explanation / Answer

T(t) = c*e-k(t) +T0

Given, T0 = 66, Initially time,t =0, T(t=0) = 195

Thus, 195 = c*e0 + 66 => c= 129

Thus, T(t) = 129e-kt + 66

putting T(t=2) = 184, we get

184 = 129*e-2k + 66

solving, e-2k = 0.915

Thus,-2k logee = loge(0.915)

-2K = -0.0891

Thus, K = 0.0446

Thus, T(t) = 129e-0.0446*t + 66

Thus,

144 = 129e-0.0446*t + 66

e-0.0446*t = 0.6045

solving, we get

-0.0446*t = - 0.5031

t = 11.28 minutes (11 mins 17 secs)

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