Solve the Problem $\mathrm { P }$ , in Thousands, of Jonesburg Is Given By

Solve the problem.
-The population $\mathrm { P }$ , in thousands, of Jonesburg is given by
$$P ( t ) = \frac { 500 t } { 2 t ^ { 2 } + 8 }$$
where $t$ is the time, in months.
Graph the function on the interval $[ 0 , \infty )$ and complete the following: $\mathrm { P } ( \mathrm { t } ) \rightarrow \quad$ as $\mathrm { t } \rightarrow \infty$

A)

$\mathrm { P } ( \mathrm { t } ) \rightarrow 50$ as $t \rightarrow \infty$ .

B)


$\mathrm { P } ( \mathrm { t } ) \rightarrow 1$ as $t \rightarrow \infty .$
C)

$\mathrm { P } ( \mathrm { t } ) \rightarrow 0$ as $\mathrm { t } \rightarrow \infty$
D)

$P ( t ) \rightarrow 45$ as $t \rightarrow \infty$ .