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 * - ur (1-)(1-) dP kP dt where k is a constant and K is the carrying capacity. Suppose that the carrying capacity K = 10000, the minimum population m = 500, 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 2 0 for what values of P is the population decreasing. Answer (in interval notation):

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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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
" - (1-)(-)
dP
= kP
dt
P
m
where k is a constant and K is the carrying capacity.
Suppose that the carrying capacity K = 10000, the minimum population m = 500, and the constant k = 0.05.
Answer the following questions.
1. Assuming P > O 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):
Transcribed Image Text: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 " - (1-)(-) dP = kP dt P m where k is a constant and K is the carrying capacity. Suppose that the carrying capacity K = 10000, the minimum population m = 500, and the constant k = 0.05. Answer the following questions. 1. Assuming P > O 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):
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