A Population of Bacteria Is Introduced into a Culture $P = 500 \left( 1 + \frac { 4 t } { 50 + t ^ { 2 } } \right)$

Multiple Choice

A population of bacteria is introduced into a culture. The number of bacteria P can be modeled by $P = 500 \left( 1 + \frac { 4 t } { 50 + t ^ { 2 } } \right)$ where t is the time (in hours) . Find the rate of change of the population when t = 2.

A) $31.55 \text { bacteria/hr }$
B) $29.15 \text { bacteria/hr }$
C) $33.65 \text { bacteria/hr }$
D) $32.75 \text { bacteria/hr }$
E) $30.25 \text { bacteria/hr }$