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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 K is 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 kelvins. (Round to two decimal places as needed.).

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 K is 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 kelvins. (Round to two decimal places as needed.).

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.1: Solutions Of Elementary And Separable Differential Equations
Problem 59E: According to the solution in Exercise 58 of the differential equation for Newtons law of cooling,...
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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, \[ \frac{dT}{dt} = K \left[ M(t) - T(t) \right] \] where \( K \) is a constant. Let \( K = 0.04 \) (min\(^{-1}\)) 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 ⬜ kelvins. (Round to two decimal places as needed.)
Transcribed Image Text: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, \[ \frac{dT}{dt} = K \left[ M(t) - T(t) \right] \] where \( K \) is a constant. Let \( K = 0.04 \) (min\(^{-1}\)) 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 ⬜ kelvins. (Round to two decimal places as needed.)
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