Consider $f(t) = 5e^{\frac{t}{3}}\sin\!\left(t\right)$.

1. The function $f(t)$ is
   
   A. continuous on $0\leq t < \infty$.
   B. discontinuous but piecewise continuous on $0\leq t < \infty$.
   C. neither.
   
   
   
2. Is $f(t)$ exponentially bounded on $0\leq t < \infty$? ? yes no
   
   
3. Does the Laplace transform of $f(t)$ exist (on some domain, i.e., for some values of s)? ? yes no