dT/dt = -k(T – Ta) where T = the temperature of the body (°C), t= time (min), k= the proportionality constant (per minute), and Ta = the ambient temperature (°C). Suppose that a cup of coffee originally has a temperature of 68°C. Use Euler's method to compute the temperature from t= 0 to 10 min using a step size of 1 min if Ta = 21°C and k = 0.1/min.
dT/dt = -k(T – Ta) where T = the temperature of the body (°C), t= time (min), k= the proportionality constant (per minute), and Ta = the ambient temperature (°C). Suppose that a cup of coffee originally has a temperature of 68°C. Use Euler's method to compute the temperature from t= 0 to 10 min using a step size of 1 min if Ta = 21°C and k = 0.1/min.
Trigonometry (MindTap Course List)
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ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Topics In Analytic Geometry
Section: Chapter Questions
Problem 33CT
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Question
Euler method (Numerical Analysis)
Newton’s law of cooling says that the temperature of a body changes at a rate proportional to the difference between its temperature and that of the surrounding medium
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- Graph
![dT/dt = -k(T – Ta)
where T = the temperature of the body (°C),
t= time (min),
k= the proportionality constant (per minute), and
Ta = the ambient temperature (°C).
Suppose that a cup of coffee originally has a temperature of 68°C. Use Euler's method to compute the temperature from t= 0 to
10 min using a step size of 1 min if Ta = 21°C and k= 0.1/min.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb765ee5c-a029-41d6-9ba1-7c3c10528579%2Fe45f7b2a-be45-4200-a6cc-cd9ec2c07758%2Foipg8s_processed.png&w=3840&q=75)
Transcribed Image Text:dT/dt = -k(T – Ta)
where T = the temperature of the body (°C),
t= time (min),
k= the proportionality constant (per minute), and
Ta = the ambient temperature (°C).
Suppose that a cup of coffee originally has a temperature of 68°C. Use Euler's method to compute the temperature from t= 0 to
10 min using a step size of 1 min if Ta = 21°C and k= 0.1/min.
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