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
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