Which of the following functions grow faster than $e^{x}$ as $x \rightarrow \infty ?$ Which grow at the same rate as $e^{x} ?$ Which grow slower?
a. $x-3 \quad$ b. $x^{3}+\sin ^{2} x$
c. $\sqrt{x} \quad$ d. $4^{x}$
e. $(3 / 2)^{x} \quad$ f. $e^{x / 2}$
g. $e^{x} / 2 \quad$ h. $\log _{10} x$