9)Let P(t)P(t) represent the amount of a certain drug, in milligrams, that is in the bloodstream at time tt hours. The rate at which the drug leaves the bloodstream is proportional to the amount of the drug in the bloodstream. The amount of the drug in the bloodstream can be modeled by dPdt=kPdPdt=kP, where kk is a constant and tt is time, in hours. At time t=0t=0, 500 milligrams of the drug was administered. At the moment when the amount of the drug in the bloodstream is 50 milligrams, the amount is decreasing at a rate of 11.5 milligrams per hour. Which of the following is an expression for P(t)P(t) ?

A

P(t)=5000.23tP(t)=5000.23t

Answer A: P of t, equals, 500 minus 0.23 t

B

P(t)=5000.232t2P(t)=5000.232t2

Answer B: P of t, equals, 500 minus the fraction 0.23, over 2, end fraction, times t squared

C

P(t)=500e0.23tP(t)=500e0.23t

Answer C: P of t, equals, 500 times e raised to the negative 0.23 t power

D P(t)=e0.23t+499

11)The size of a population is modeled by the function P that satisfies the logistic differential equation dPdt=110P15000P2, where t is measured in months and P(0)=50. What is the size of the population at the moment when the population is growing most rapidly?

A

50

Answer A: 50

B

250

Answer B: 250

C

500

Answer C: 500

D 2500