smc

We proceed by using AM-GM. We get $\frac{(2^t-3t)+3t}{2}$ $\ge \sqrt{(2^t-3t)(3t)}$. Thus, squaring gives us that $4^{t-1}\ge (2^t-3t)(3t)$. Remembering what we want to find, we divide both sides of the inequality by the positive amount of $\frac{1}{3\cdot 4^t}$. We get the maximal values as $\boxed{\frac{1}{12}}$, and we are done.