dT Newton's law of cooling states that the rate of change in the temperature T(t) of a body is proportional to the difference between the temperature of the medium M(t) and the temperature of the body. That is, = K[M(t) - T(t)), where dt -1 Kis a constant. Let K= 0.04 (min)' and the temperature of the medium be constant, M(t) = 290 kelvins. If the body is initially at 352 kelvins, use Euler's method with h =0.1 min to approximate the temperature of the body after (a) 30 minutes and (b) 60 minutes. (a) The temperature of the body after 30 minutes is 308.62 kelvins. (Round to two decimal places as needed.) (b) The temperature of the body after 60 minutes is kelvins. (Round to two decimal places as needed.)

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Chapter1: Units, Trigonometry. And Vectors
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Newton's law of cooling states that the rate of change in the temperature T(t) of a body is proportional to the difference between the temperature of the medium M(t) and the temperature of the body. That is, = K[M(t) - T(t)), where
dt
Kis a constant. Let K= 0.04 (min)' and the temperature of the medium be constant, M(t) = 290 kelvins. If the body is initially at 352 kelvins, use Euler's method with h =0.1 min to approximate the temperature of the body after (a)
30 minutes and (b) 60 minutes.
(a) The temperature of the body after 30 minutes is 308.62 kelvins.
(Round to two decimal places as needed.)
(b) The temperature of the body after 60 minutes is
kelvins.
(Round to two decimal places as needed.)
Transcribed Image Text:dT Newton's law of cooling states that the rate of change in the temperature T(t) of a body is proportional to the difference between the temperature of the medium M(t) and the temperature of the body. That is, = K[M(t) - T(t)), where dt Kis a constant. Let K= 0.04 (min)' and the temperature of the medium be constant, M(t) = 290 kelvins. If the body is initially at 352 kelvins, use Euler's method with h =0.1 min to approximate the temperature of the body after (a) 30 minutes and (b) 60 minutes. (a) The temperature of the body after 30 minutes is 308.62 kelvins. (Round to two decimal places as needed.) (b) The temperature of the body after 60 minutes is kelvins. (Round to two decimal places as needed.)
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