Math
posted by Jenny .
It is known that if the deer population falls below a certain level, m, then the deer will become extinct. It is also known that is the deer population goes above the maximum carrying capacity, M, the population will decrease to M.
(a) Discuss the reasonableness of the following model for the growth rate of the deer population as a function of time: dP/dt = kP(MP)(Pm), where P is the population and k is a constant of proportionality.
(b) Explain how this growth rate model differs from the logistical model dP/dt = kp(MP) Is it better or worse than the logistical model?
(c) Show that if P > M for all t, then the limit as P(t) approached infinity is M.
(d) Assuming m < P < M for all t, briefly explain the steps you would use to solve the differential equation.
(e) What are the equilibrium point of the model? Explain the dependence of the equilibrium level of P on the initial conditions. How many deer hunting permits should be issued?
Respond to this Question
Similar Questions

math
The model N = 10(4+3t)/1.25 describes the number of deer (N) in a park t years after 40 deer are introduced into the region. Approximately how long will it take the deer population to reach 224? 
science
why do you think the deer population was only 4,00 in 1905 when the carrying capacity of the rangeland could support 30,000 deer or more. I don't understand why a population could be so far below the carrying capacity. 
Science  HW qs. check
6. What happened to the population of deer when the wolves were introduced? 
algebra
Data from a deer count in forested area show that an estimated 3.16 x 10^3 deer inhabit 1.998 x 10^4 acres of land. What is the density of the deer population? 
MATH
A protected area was stocked with 1500 deer of a certain species in 1995. The deer population in 2010 was found to be 3350 deer. Let t be the number of years after 1195. Find the deer population at t=3 
Calculus
the population of deer in a certain area of cabarrus county grows proportional to itself. the population of deer in 2000 was found to be 45, and by 2008 the population had grown to 65. Find the growth constant k(rounded to 6 decimal … 
Math
A herd of 100 deer is introduced onto a small island. At first the herd increases rapidly, but eventually food resources dwindle and the population declines. Suppose the number of deer, N(t), after t years is described by the polynomial … 
math
Suppose that the population of deer in a state is 19,900 and is growing 3% each year. Predict the population after 10 years. (1 point) A.about 274,338 deer B.about 26,744 deer**** D.about 597,000 deer C.about 204,970 deer i need help … 
college algebra
QUESTION 14 The game commission introduces 100 deer into newly acquired state game lands. The population N of the herd is modeled by where t is the time in years. Find the populations when t=40. (Round your answer to the nearest whole …