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MATH 102 Lecture 31: Week 11, Lecture 30 and Week 12, Lecture 31 - Euler's Method and Disease Modelling

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redfox265
30 Nov 2016
School
UBC
Department
Mathematics
Course
MATH 102
Professor
Eric Cytrynbaum

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Euler's Method and Infection Modelling
November 21, 2016 10:01 AM
MATH 102 Page 1
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Related Questions


1 pt) Newton's Law of Cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings. Suppose t is time, T is the temperature of the object, and Ts is the surrounding temperature. The following differential equation describes Newton's Law

dT/dt=k(T-Ts),

where k is a constant.

Suppose that we consider a 92(oC)cup of coffee in a 24(oC) room. Suppose it is known that the coffee cools at a rate of 2(oC)/min. when it is 70(oC). Answer the following questions.

Find the constant k in the differential equation.
Answer (in per minute): k=

2. What is the limiting value of the temperature?
Answer (in Celsius): T=

3. Use Euler's method with step size h=2 minutes to estimate the temperature of the coffee after 10 minutes.
Answer (in Celsius): T(10)?

Am sorry to ask a lot f questions today