Answer
(a) $y=16e^{-0.1t}cos(24\pi t)$
(b) see graph.
Work Step by Step
(a) Given $k=16,c=0.1,f=12$, we have $\omega=2\pi f=24\pi$, and
since the maximum happens at $t=0$, we use the $cos$ function.
The function that models this motion is
$y=ke^{-ct}cos(\omega t)=16e^{-0.1t}cos(24\pi t)$
(b) The above function can be graphed as shown in the figure.
