This phenomenon is modeled with a differential equation, and that equation may be solved to give T(t) = TA + [T0 − TA]b t where T(t) is the varying temperature of the object at a given time, t, TA is the surrounding ambient temperature, T0 is the initial temperature of the object, and b is a constant that depends on the material the object is composed of and how fast it heats or cools. Suppose you decided to make a cup of hot tea heated to 220 F in the kitchen that is at 70 F.

1.Solve the above equation for the constant b.

2.If the cup of hot tea cooled to 170 F in 10 minutes, find the value of the constant b in the above equation. Express your answer to 5 decimal places.

3.Solve the above equation for t.

4.Suppose you like your hot tea at the tepid temperature of 100 F. How long, to the nearest minute, will you have to wait until it cools to this temperature?

To go along with your hot tea, you take a frozen apple pie from the freezer and place it in the oven preheated to 350 F. Assume the freezer is at 32 F.

5.If the apple pie comes to a temperature of 100 F in 20 minutes, find the value of the constant b in the above equation. Express your answer to 5 decimal places.

6.How long will it take for the pie to reach its final temperature of 200 F?

7. The pie is taken out of the oven and set on a table in a room at 70 F. In 10 minutes, it has cooled to 180 F. However, the pie must cool to 120 F before it is ready to eat. How much longer will you have to wait?