# Suppose a cup of coffee is at 100 degrees Celsius at time t = 0, it is at 70 degrees

at t = 10 minutes, and it is at 50 degrees at t = 20 minutes. Compute the ambient temperature.

So in the book I was given Newton's Heat equation.

dT/dt=k(A-T) where T is temperature of the coffee. t is time. A is the ambient temperature.

This is a seperable equation so I isolated k to one side with dt and dT/(A-T)

When I took the integral of both sides I got

ln(A-T)=kt+C

which is then

A=e^(kt+C)+T

How do I find ambient temperature or k or C? I am very confused and cannot get past this step.

Thanks!