Solve the Problem $P ( t )$ Of a Bacteria Culture Is Given By

Solve the problem.
-The population $P ( t )$ of a bacteria culture is given by $P ( t ) = - 1,500 t ^ { 2 } + 48,000 t + 18,000$ , where $t$ is the time in hours after the culture is started. Determine the time(s) at which the population will be greater than 388,500 organisms.

A) The population will be greater than 388,500 organisms from $19 \mathrm { hr }$ after the culture is started.
B) The population will be greater than 388,500 organisms from $25 \mathrm { hr }$ after the culture is started.
C) The population will be greater than 388,500 organisms between $13 \mathrm { hr }$ and $25 \mathrm { hr }$ after the culture is started.
D) The population will be greater than 388,500 organisms between $13 \mathrm { hr }$ and $19 \mathrm { hr }$ after the culture is started.