Solve the Problem $N(t)=5 t \sqrt{3 t+12}-6$ Where $t$ Represents Time in Hours After the Beginning of an Experiment

Multiple Choice

Solve the problem.
-The total number of bacteria (in millions) present in a culture is given by $N(t) =5 t \sqrt{3 t+12}-6$ where $t$ represents time in hours after the beginning of an experiment. Find the rate of change of the population of bacteria with respect to time for $t=3$ .

A) 42.55
B) 21.82
C) 1.31
D) 27.82