AMC 12 2020b Problem 22

What is the maximum value of $\frac{(2^t-3t)t}{4^t}$ for real values of $t?$

\textbf{(A)}\ \frac{1}{16} \textbf{(B)}\ \frac{1}{15} \textbf{(C)}\ \frac{1}{12} \textbf{(D)}\ \frac{1}{10} \textbf{(E)}\ \frac{1}{9}