Solve the problem.
-The population P(t) of a culture of bacteria is given by $$P ( t ) = - 1,840 t ^ { 2 } + 81,000 t + 10,000$$ where t is the time in hours since the culture was started. Determine the time at which the population is at a
Maximum. Round to the nearest hour.
A) 22 hr
B) 44 hr
C) 9 hr
D) 18 hr

Question

Quizplus · Accepted Answer

The population is at a maximum when the derivative of the population function is equal to zero.$$\frac{dP}{dt} = -3,680t + 81,000$$$$-3,680t + 81,000 = 0$$$$t = 22$$Therefore, the population is at a maximum at 22 hours.

Solve the Problem P(t)=−1,840t2+81,000t+10,000P ( t ) = - 1,840 t ^ { 2 } + 81,000 t + 10,000P(t)=−1,840t2+81,000t+10,000

Solve the Problem $P ( t ) = - 1,840 t ^ { 2 } + 81,000 t + 10,000$