There is considerable evidence to support the theory that for some species there

Question

There is considerable evidence to support the theory that for some species there is a minimum population m such that the species will become extinct if the size of the population falls below m This condition can be incorporated into the logistic equation by introducing the factor

(1-(m/p)) Thus the modified logistic model is given by the differential equation

where k is a constant and k is the carrying capacity.

Suppose that the carrying capacity k = 10000 the minimum population m = 800 and the constant  k = 0.05 Answer the following questions.

1. Assuming P >= 0 for what values of P is the population increasing.
Answer (in interval notation):

2. Assuming P >= 0 for what values of P is the population decreasing.
Answer (in interval notation):

Explanation / Answer

for first case

dp/dt >0

=> kP (1- (P/K)) (1-(m/P)) >0

(1- (P/K)) (1-(m/P)))>0 and p>o

k>p and p>m or k<p and p<m k=10000, m=800

p belongs (800,10000)

for second case

dp/dt< o

i.e    kP (1- (P/K)) (1-(m/P)) <0

=> p= (0,800)U(10000,infinity)

p= (800,10000)

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