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, dT -=K[M(t)- T(t)], where K is a constant. Let K = 0.04 (min) 1 and the temperature of the medium be constant, dt M(t) = 294 kelvins. If the body is initially at 364 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, dT -=K[M(t)- T(t)], where K is a constant. Let K = 0.04 (min) 1 and the temperature of the medium be constant, dt M(t) = 294 kelvins. If the body is initially at 364 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.)
Chapter6: Exponential And Logarithmic Functions
Section6.1: Exponential Functions
Problem 60SE: The formula for the amount A in an investmentaccount with a nominal interest rate r at any timet is...
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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,
dT
-= K[M(t) - T(t)], where K is a constant. Let K = 0.04 (min) ¹ and the temperature of the medium be constant,
dt
M(t) = 294 kelvins. If the body is initially at 364 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
(Round to two decimal places as needed.)
kelvins.
60min=](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3596ba0c-593e-41eb-bfdd-7cee262dea67%2Fb31e0b8c-c63b-4664-974b-97dac4ee8408%2Ftegp9dv_processed.png&w=3840&q=75)
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,
dT
-= K[M(t) - T(t)], where K is a constant. Let K = 0.04 (min) ¹ and the temperature of the medium be constant,
dt
M(t) = 294 kelvins. If the body is initially at 364 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
(Round to two decimal places as needed.)
kelvins.
60min=
Expert Solution
Step 1
Given Data:
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,
Where K is constant.
To Find:
The temperature of the body after 30 minutes and 60 minutes.
Step by step
Solved in 6 steps
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