Question: A diligent, hardworking student has a bicycle with a slow leak in the front
tire but has been too busy studying for exams to get the tire fixed. Assume
that the pressure in the tire decreases at a rate proportional to the
difference between the atmospheric pressure (15 lbs/square-inch) and the tire
pressure. Monday at 6:00 PM the tire pressure was pumped up to 85
lbs/square-inch and by Tuesday at 6:00 PM the tire pressure was down to 75
lbs/square-inch.

a) Write a differential equation that describes the rate at which the tire's
pressure P is changing.

b) Solve for the differential equation in part a) for P(t).

c) If the recommended minimum tire pressure is 40 lbs/square-inch, how long
can the student wait before pumping up the tire again?