1. At time t = 0 minutes, the temperature of a cup of coffee is 180 degrees Fahrenheit. Left in a room

whose temperature is 70 degrees Fahrenheit, the coffee cools so that its temperature function T(t),

also measured in degrees Fahrenheit, satisfies the differential equation * = - T +35.

(a) Find an expression for T(t) using the initial condition T(0) = 180.

(b) Find lim T(t). Explain what this limit means in the context of the problem.

(c) At what time t is the temperature of the coffee decreasing at the rate of 15 degrees Fahrenheit per

minute? How hot is the coffee at that point? Indicate units of measurement.