I'm not sure how you got B=70 but that is not correct.
You have 3 equations to solve for the 3 unknowns
1. Jane makes coffee with water from an urn which is at a temperature of 95 deg C.
At time t=0 the temperature is 95
2. Jane carries a thermometer with her at all times and notes that 7 minutes later her coffee has cooled to 70 deg C.
At time t=7 the temperature is 70
3. As time time tends to infinity the temperature of the coffee becomes the same as the room temperature.
The equation for the third one is
There are three cases for k,
k>1 this would cause the temperature to grow to infinity as time passes which is clearly wrong
k=1 this would mean that T(t)=A+B which is constant, clearly temperature is not constant so k cannot be 1
k<1 is the only reasonable case left
If k<1 then so simplifies to
Now you have A, use the other two equations to find B and k. Once you have them the second part of your question should follow easily.