Question

9. (10 points) Suppose you are going to bake sweet potatoes for dinner. You preheat the oven to 400 degrees Fahrenheit. At time t = 0, you put the sweet potatoes in the oven. a. Use Newton's Law of Cooling to write down a differential equation that describes the temperature of your sweet potatoes T over time. b. Determine the equilibrium solution of the differential equation in part (a). c. Determine the general solution of the differential equation in part (a). d. The initial temperature of the sweet potatoes is the same as the temperature of your kitchen, about 68 degrees Fahrenheit. After baking for 25 minutes, you check the temperature of the sweet potatoes and they are about 310 degrees Fahrenheit. Determine the solution of the differential equation that satisfies these conditions. e. Approximately how long will it take for the sweet potatoes to reach a temperature of 375 degrees Fahrenheit?

          9. (10 points) Suppose you are going to bake sweet potatoes for dinner. You preheat the oven to 400 degrees Fahrenheit. At time t = 0, you put the sweet potatoes in the oven.
a. Use Newton's Law of Cooling to write down a differential equation that describes the temperature of your sweet potatoes T over time.
b. Determine the equilibrium solution of the differential equation in part (a).
c. Determine the general solution of the differential equation in part (a).
d. The initial temperature of the sweet potatoes is the same as the temperature of your kitchen, about 68 degrees Fahrenheit. After baking for 25 minutes, you check the temperature of the sweet potatoes and they are about 310 degrees Fahrenheit. Determine the solution of the differential equation that satisfies these conditions.
e. Approximately how long will it take for the sweet potatoes to reach a temperature of 375 degrees Fahrenheit?

Added by David L.

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