Euler"s method: estimate the temperature of the coffee
In Exercise 14 in Section 7.1 we considered a 95°C cup of coffee in a 20°C room. Suppose it is known that the coffee cools at a rate of 1°C per minute when itstemperature is 70°C. (a) What does the differential equation become in this case? (b) Sketch a direction field and use it to sketch the solution curve for the initial-value problem. What is the limiting value of the temperature? (c) Use Euler"s method with step size h=2 minutes to estimate the temperature of the coffee after 10 minutes.