Question

"A solar hot-water heating system consists of a hot-water tank and a solar panel. The tank is well insulated and has a time constant of 64 hr. The solar panel generates 2000 Btu/hr during the day, and the tank has a heat capacity of 2°F per thousand Btu. If the water in the tank is initially 110°F and the room temperature outside the tank is 80°F what will be the temperature in the tank after 12 hrs of sunlight"
please show full work (maybe a pic) and answer ASAP giving tons of points for it

Answer 1

T(t)=e−kt(∫ekt[KM(t)+H(t)+U(t)]dt+C) M is the outside temperature, H is other things that affect temperature in the tank(0 in this case), and U is the solar panel. K comes from the time constant, and should be the inverse of the time constant I believe. T is temperature, t is time.

T(t)=e−164t(∫e164t[164(80)+4t]dt After integrating I keep getting −16304+256t+Ce−164t I calculate C to be 16414 setting t equal to 0 and using the initial conditions