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 dP dt KP (1-P) (1-7) = where k is a constant and K is the carrying capacity. Suppose that the carrying capacity K = 10000, the minimum population m = 600, and the constant k = 0.2. 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):
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 dP dt KP (1-P) (1-7) = where k is a constant and K is the carrying capacity. Suppose that the carrying capacity K = 10000, the minimum population m = 600, and the constant k = 0.2. 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):
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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
P
m
-- KP (1-K) (¹-P)
=
dP
dt
where k is a constant and K is the carrying capacity.
=
Suppose that the carrying capacity K = 10000, the minimum population m = 600, and the constant k
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):
0.2.
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