Answer
Diverges
Work Step by Step
\begin{aligned}
\int_{4}^{\infty} e^{3 x} d x &=\lim _{R \rightarrow \infty} \int_{4}^{R} e^{3 x} d x \\ &=\lim _{R \rightarrow \infty}\left.\frac{e^{3 x}}{3}\right|_{4} ^{R} \\ \\ &=\lim _{R \rightarrow \infty}\left(\frac{e^{3 R}}{3}-\frac{e^{12}}{3}\right)\\
&= \infty \end{aligned}
The integral diverges.
