Suppose that the temperature T inside a mountain cab in behaves according to Newton’s law...

Suppose that the temperature T inside a mountain cab in behaves according to Newton’s law of cooling, as in

where t is measured in hours and the ambient temperature A outside the cabin varies sinusoidally with a period of 24hours. At 6 A.M., the ambient temperature outside is at a minimum of 40°F. At 6 p.m., the ambient temperature isat a maximum of 80°F.

(a) Adjust equation to model the sinusoidal nature of the ambient temperature.

(b) Suppose that at midnight the temperature inside the cabin is 50°F. Solve the resulting initial value problem. Hint: You can simplify the calculation by letting gt = 0 represent midnight. You might also consider technique suggested in Exericse.

(c) Sketch the graph of the temperature inside the cab in. On the same coordinate system, superimpose the plot of the ambient temperature outside the cabin. Comment on the appearance of the plot.