Homework: 5.6 Applications and Models: Growth, Decay and Com Score: 0 of 1 pt 5o

Question

Homework: 5.6 Applications and Models: Growth, Decay and Com Score: 0 of 1 pt 5of7"compete) ? Hw Score: 4524%,117of7pts 5.6.19 According to Newton's Law of Cooling, t a body with temperature T, is placed in wurroundings with tempenature To. diferent from that of T, the body wll ofher coel or warm to peratue A cup of cofee with temperature 125*F is placed in a troezer with tempereture O"F.After 15 minutes, the temperature of the cofe 3 F. Use Newton's Law of Cooling to frd th Round to the nearest intager. Enter your answer in the Al parts showing 133.. caps lock NM

Explanation / Answer

As per the Newton’s law of cooling, if a body with temperature T1, is placed in surroundings with temperature T0, then it either cools down or warms up to the temperature T(t) after t minutes, where T(t) = T0 +(T1-T0)e-kt where k is the coefficing of cooling.

Here, T1, the temperature of the cup of coffee is 1250 F and T0, the temperature of the freezer is 00 F. After 15 minutes, the temperature of coffee is 320 F. Hence 32 = 0+(125-0)e-15k or, e-15k = 32/125. Now on taking natural logarithm of both the sides, we get -15k ln e = ln(32/125) or, -15k = -1.362577835 so that k = 1.362577835/15 = 0.090838522.

Thus, after 20 minutes, the coffee’s temperature will be 0+(125-0)e-20*0.090838522 = 125e-1.816770446 = 125*0.162549867 = 20.320 F

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