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.

when ,

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.