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. Th 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 where k is a constant and K is the carrying capacity. Suppose that the carrying capacity K = 20000, the minimum population m = 500, 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. Th 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 where k is a constant and K is the carrying capacity. Suppose that the carrying capacity K = 20000, the minimum population m = 500, 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 m/P). Thus the modified logistic model is given by the differential equation
dP
P-AP (1-²) (1-7)
kP
dt
K
where k is a constant and K is the carrying capacity.
Suppose that the carrying capacity K = 20000, the minimum population m = 500, 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):
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