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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.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.6: Quadratic Functions
Problem 37E
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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.
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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