Answer
$t=\frac{k}{4}$ where $k=0, \pm1, \pm2, ...$
Work Step by Step
Step 1. With $f(t)=0$, we setup the equation as $2^{-0.2t}sin4\pi t=0$
Step 2. As $2^{-0.2t}\gt0$ for all real $t$, the above equation becomes $sin4\pi t=0$
Step 3. The general solutions for the above equation are $4\pi t=k\pi$ where $k$ is any integer, this leads to $t=\frac{k}{4}$
