A Population of Bacteria Is Introduced into a Culture $P = 275 \left( 1 + \frac { 7 t } { 47 + t ^ { 2 } } \right)$

Multiple Choice

A population of bacteria is introduced into a culture. The number of bacteria P can be modeled by $P = 275 \left( 1 + \frac { 7 t } { 47 + t ^ { 2 } } \right)$ where t is the time (in hours) . Find the rate of change of the population when $t = 5.00$ .

A) 87.50 units per dollar
B) 1.17 units per dollar
C) 8.17 units per dollar
D) 8.91 units per dollar
E) 12.50 units per dollar