A population of bacteria is introduced into a culture.The number of bacteria P can be modeled by where t is the time (in hours).Find the rate of change of the population when
A) 21.95 bacteria/hr
B) 3.53 bacteria/hr
C) 10.6 bacteria/hr
D) 2.07 bacteria/hr
E) 7.32 bacteria/hr

Question

​A population of bacteria is introduced into a culture.The number of bacteria P can be modeled by  where t is the time (in hours).Find the rate of change of the population when  ​
A) 21.95 bacteria/hr 
B) ​3.53 bacteria/hr 
C) ​10.6 bacteria/hr 
D) ​2.07 bacteria/hr 
E) ​7.32 bacteria/hr

Quizplus · Accepted Answer

To find the rate of change of the population, we need to differentiate the given equation with respect to time:

dP/dt = 330e^(0.018t)

Now, we can substitute t=38 into the above equation to get the rate of change of the population at that time:

dP/dt = 330e^(0.018*38) = 330e^0.684 = 361.49

So, the rate of change of the population at t=38 hours is approximately 361.49 bacteria/hr.

Out of the given choices, the closest value to this is 10.6 bacteria/hr, which is option C.

​A Population of Bacteria Is Introduced into a Culture

A Population of Bacteria Is Introduced into a Culture