You can put this solution on YOUR website! 2^t is an exponential function with a horizontal asymptote at 0. Its domain is t is all reals.
Since it is always positive, there exist values of t that don't work.
If t = 0, then g(t) = 0
if t > 0 , then g(t) will be no solution.
The domain of the function is then
t <= 0.