The total number P of prey taken by a predator depends on the availability of prey. C. S. Holling proposed a function of the form P = cn/(1+ dn) to model the number of prey taken in certain situations. Here n is the density of prey available, and c and d are constants that depend on the organisms involved as well as on other environmental features. Holling took data gathered earlier by T. Burnett on the number of sawfly cocoons found by a small wasp parasite at given host density. In one such experiment conducted, Holling found the relationship 21.96 1+2.41n where P is the number of cocoons parasitized and n is the density of cocoons available (measured as number per square inch). (a) Draw a graph of P versus n. Include values of n up to 2 cocoons per square inch. P 15 10 15 10 5 0.5 1.0 1.5 2.0 n P 15 10 15 10 0.5 MacBook Air 1.0 1.5 WebAssign Plot 2.0 n

Algebra and Trigonometry (6th Edition)
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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SC
The total number P of prey taken by a predator depends on the availability of prey. C. S. Holling proposed a function of the form P = cn/(1+ dn) to model the number of prey taken in certain
situations. Here n is the density of prey available, and c and d are constants that depend on the organisms involved as well as on other environmental features. Holling took data gathered earlier by T.
Burnett on the number of sawfly cocoons found by a small wasp parasite at given host density. In one such experiment conducted, Holling found the relationship
21.96m
1+2.41n'
where P is the number of cocoons parasitized and n is the density of cocoons available (measured as number per square inch).
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Transcribed Image Text:SC The total number P of prey taken by a predator depends on the availability of prey. C. S. Holling proposed a function of the form P = cn/(1+ dn) to model the number of prey taken in certain situations. Here n is the density of prey available, and c and d are constants that depend on the organisms involved as well as on other environmental features. Holling took data gathered earlier by T. Burnett on the number of sawfly cocoons found by a small wasp parasite at given host density. In one such experiment conducted, Holling found the relationship 21.96m 1+2.41n' where P is the number of cocoons parasitized and n is the density of cocoons available (measured as number per square inch). (a) Draw a graph of P versus n. Include values of n up to 2 cocoons per square inch. 1 P= A F1 Q N 2 P 15 10 P 15 10 * F2 W S X 0.5 #3 80 F3 E D 1.0 C $ 4 F4 R 1.5 F 01 2 % 5 V 2.0 FS T G 18 15 O 10 P 15 10 < 6 P MacBook Air B 244 FO 0.5 Y & 7 44 F7 I 1.0 U N 1.5 WebAssign Plot * 8 DII FB I 2.0 H J K M ( 9 n DD F9 0 < ) I 0 L 4 F10 P > : ; 3 * F11 { J + = [ 21 ? 41) F12 .. I } I 1 delete L
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Transcribed Image Text:! 1 3 Q A N 10 O FI P 15 O 10 Need Help? Read It 2 5 cocoons 0.5 F2 W S 0.5 # 3 80 F3 1.0 1.5 E D 1.0 X C $ 1.5 4 888 F4 R (b) What density of cocoons will ensure that the wasp will find and parasitize 7 of them? (Round your answer to one decimal place.) cocoon(s) per square inch F 2.0 % 5 2.0 (c) There is a limit to the number of cocoons that the wasp is able to parasitize no matter how readily available the prey may be. What is this upper limit? (Round your answer to the nearest whole number.) V n A F5 T 10 G 15 O 10 6 P A 5 B 0.5 F6 0.5 MacBook Air Y H & 7 80 F7 1.0 1.0 U N * CO 1.5 8 1.5 J DII F8 I 2.0 M 2.0 ( 9 n K n DD F9 O < ) 0 L 4 F10 P V : ; ( F11 { +11 [ = ? : 4) F12 I } I 1
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