> I have taught AB Calc for 18 years, but am teaching BC for the > first time this year. I am trying to do the BC practice exam that > was published last spring on the AP Audit section of The College > Board website. I am stuck on problem #84. Could someone please > help me? Here is the problem. > > The rate of change, dP/dt, of the number of people on an ocean > beach is modeled by a logistic differential equation. The maximum > number of people allowed on the beach is 1200. At 10 a.m., the > number of people on the beach is 200 and is increasing at the rate > of 400 people per hour. Which of the following differential > equations describes the situation? The correct answer is C. > > (A) dP/dt = (1/400)(1200-P)+ 200 > (B) dP/dt = (2/5)(1200-P) > (C) dP/dt = (1/500)P(1200-P) > (D) dP/dt = (1/400)P(1200-P) > (E) dP/dt = 400P(1200-P) >
The general equation for logistic growth is dP/dt = kP(C - P) where C is the carrying capacity.
Your given information is: C = 1200, P = 200, dP/dt = 400. You need to find k.
dP/dt = kP(C - P) 400 = k(200)(1200 - 200) 400 = 200000 k k = 1/500