Assume that N(t) denotes the density of an insect species at time t and P(t) denotes the density of its predator at time t. The insect species is an agricultural pest, and its predator is used as a biological control agent. Their dynamics are given below by the system of differential equations. Complete parts (a) through (c). dN = 7N - 5PN dt dP = 4PN - P dt ..... (a) Explain why dN = 7N describes the dynamics of the insect in the absence of the predator. dt If there are no predators present, then P(t) = for all t. Substitute P = in the given differential dN equations to get dt So in the absence of the predators, the above equation describes the dynamics of the insect population. dN Solve the equation, dt N(t) = (Type an expression using t as the variable.) Describe what happens to the insect population in the absence of the predator. In the o boone dotor tho in uletion
Assume that N(t) denotes the density of an insect species at time t and P(t) denotes the density of its predator at time t. The insect species is an agricultural pest, and its predator is used as a biological control agent. Their dynamics are given below by the system of differential equations. Complete parts (a) through (c). dN = 7N - 5PN dt dP = 4PN - P dt ..... (a) Explain why dN = 7N describes the dynamics of the insect in the absence of the predator. dt If there are no predators present, then P(t) = for all t. Substitute P = in the given differential dN equations to get dt So in the absence of the predators, the above equation describes the dynamics of the insect population. dN Solve the equation, dt N(t) = (Type an expression using t as the variable.) Describe what happens to the insect population in the absence of the predator. In the o boone dotor tho in uletion
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:Assume that N(t) denotes the density of an insect species at time t and P(t) denotes the density of its
predator at time t. The insect species is an agricultural pest, and its predator is used as a biological control
agent. Their dynamics are given below by the system of differential equations. Complete parts (a) through
(c).
dN
= 7N - 5PN
dt
dP
= 4PN - P
dt
.....
(a) Explain why
dN
= 7N describes the dynamics of the insect in the absence of the predator.
dt
If there are no predators present, then P(t) =
for all t. Substitute P =
in the given differential
dN
equations to get
dt
So in the absence of the predators, the above equation describes the
dynamics of the insect population.
dN
Solve the equation,
dt
N(t) =
(Type an expression using t as the variable.)
Describe what happens to the insect population in the absence of the predator.
In the absence of the predator, the insect population
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