Find the Slowest Growing and the Fastest Growing Functions as X→∞

Multiple Choice

Find the slowest growing and the fastest growing functions as x→∞ .
- $$\begin{array} { l } y = 2 x ^ { 2 } + 9 x \\y = e ^ { x } \\y = e ^ { x } / 6 \\y = \log _ { 4 } x\end{array}$$

A) Slowest: $y = \log _ { 4 } x$
Fastest: $\mathrm { y } = \mathrm { e } ^ { \mathrm { X } }$
B) Slowest: $2 x ^ { 2 } + 9 x$
Fastest: $\mathrm { y } = \mathrm { e } ^ { \mathrm { x } }$
C) Slowest: $y = e ^ { x } / 6$
Fastest: $2 x ^ { 2 } + 9 x$
D) Slowest: $y = \log _ { 4 } x$
Fastest: $\mathrm { y } = \mathrm { e } ^ { \mathrm { x } }$ and $\mathrm { y } = \mathrm { e } ^ { \mathrm { x } } / 6$ grow at the same rate.