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 measure in degrees Fahrenheit, the differential equation dT/dt = -1/2T + 35

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

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.

Hey lysskli.

Hint: You have a separable DE where dT/[-0.5T + 35] = dt. This means you can integrate and collect terms to get T(t) = f(t) for some function f. What do you think the anti-derivative of 1/(-0.5T + a) will be (where a is a constant)?

I honestly don't know. Do I take the integral?

Yes integrate both sides: one side will be in terms of dT and the other in terms of dt. Once you do that then get T as a function of t and you're done.

$\frac{dt}{dT}=\frac{1}{-0.5T+35}$