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## Homework Statement

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 96C cup of coffee in a 25C room. Suppose it is known that the coffee cools at a rate of 2C/min. when it is 70C Answer the following questions.

1. 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)

Can someone help me get started with this problem? Thanks