49. Predation Rate The prey-density responses of some predators are sigmoidal: the number of prey attacked has a sigmoidal shape when plotted as a function of prey density. If we denote the num- ber of nearby prey by N, and the handling time of each prey item by Th, then the rate of prey attacks per predator as a function of N and T, can be expressed as bN? P(N, T) = 1+cN +bT,N² where b and c are positive constants. (a) Investigate how an increase in the prey density N affects the function P(N, Th). (b) Investigate how an increase in the handling time T affects the function P(N, Th). (c) Graph P(N, T,) as a function of N when T = 0.2 hours, b = 0.8, andc= 0.5.
49. Predation Rate The prey-density responses of some predators are sigmoidal: the number of prey attacked has a sigmoidal shape when plotted as a function of prey density. If we denote the num- ber of nearby prey by N, and the handling time of each prey item by Th, then the rate of prey attacks per predator as a function of N and T, can be expressed as bN? P(N, T) = 1+cN +bT,N² where b and c are positive constants. (a) Investigate how an increase in the prey density N affects the function P(N, Th). (b) Investigate how an increase in the handling time T affects the function P(N, Th). (c) Graph P(N, T,) as a function of N when T = 0.2 hours, b = 0.8, andc= 0.5.
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:49. Predation Rate The prey-density responses of some predators
are sigmoidal: the number of prey attacked has a sigmoidal shape
when plotted as a function of prey density. If we denote the num-
ber of nearby prey by N, and the handling time of each prey item
by Th, then the rate of prey attacks per predator as a function of
N and T can be expressed as
bN?
P(N, Th) =
1+cN + bT,N²
where b and c are positive constants.
(a) Investigate how an increase in the prey density N affects the
function P(N, Th).
(b) Investigate how an increase
the function P(N, T).
the handling time T, affects
(c) Graph P(N, T,) as a function of N when T = 0.2 hours,
b = 0.8, and c 0.5.
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