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Problem 1: The ornithologist David Lack (1954) proposed that the number of eggs laid per parent, aka the "clutch size", is determined by a trade-off between the number of eggs laid and the survival of the chicks. If the clutch size is b the cycle diagram for of birds at time 4, N(1), is given by: N(t + 1) = N"(t) N(t) census Eggs laid N't) = b N(t) Chick survival N"(t) = N'(t)(1- sb) = N (t)b(1- sb) The parameter s here is the strength of the Lack' trade-off between offspring number and juvenile survival. A. Write a recursion equation for the number of birds at time t corresponding to the cycle diagram. N°Ct) is N'(t) (I-sb) %3D NtSb(I-sb) %3D B. If there at 10 birds in the population at time 0 and the clutch size is 6 5 and the strength of the trade-olf is s = 0.1, find the numerical solution for N() for {0, 1,..10} NCt) Nt t1) = Nt)b(1- sb) N, = 10 (s )(1- (0.1 ×5)) = 25 Na = 25(5)(1- (o.1 x5)) = 625 N3 =62.5(S)(1- (0.1 XS)) = 156, 25 10 25 62.5 %3D 156.25 %3D 3१०. ०25 976 5625 2441.41 6103.52 15258 789 30140,97 1 10 1 95367.4

Problem 1: The ornithologist David Lack (1954) proposed that the number of eggs laid per parent, aka the "clutch size", is determined by a trade-off between the number of eggs laid and the survival of the chicks. If the clutch size is b the cycle diagram for of birds at time 4, N(1), is given by: N(t + 1) = N"(t) N(t) census Eggs laid N't) = b N(t) Chick survival N"(t) = N'(t)(1- sb) = N (t)b(1- sb) The parameter s here is the strength of the Lack' trade-off between offspring number and juvenile survival. A. Write a recursion equation for the number of birds at time t corresponding to the cycle diagram. N°Ct) is N'(t) (I-sb) %3D NtSb(I-sb) %3D B. If there at 10 birds in the population at time 0 and the clutch size is 6 5 and the strength of the trade-olf is s = 0.1, find the numerical solution for N() for {0, 1,..10} NCt) Nt t1) = Nt)b(1- sb) N, = 10 (s )(1- (0.1 ×5)) = 25 Na = 25(5)(1- (o.1 x5)) = 625 N3 =62.5(S)(1- (0.1 XS)) = 156, 25 10 25 62.5 %3D 156.25 %3D 3१०. ०25 976 5625 2441.41 6103.52 15258 789 30140,97 1 10 1 95367.4

Advanced Engineering Mathematics
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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IQ2 report all ansuwers to 2 significant digits Student Narme (#): Hui Zhi 301454741 Problem 1: The ornithologist David Lack (1954) proposed that the number of eggs laid per parent, aka the "clutch size", is determined by a trade-off between the number of eggs laid and the survival of the chicks. If the clnteh size is b the cycle diagram for of birds at time 1, N(1), is given by: N(t + 1) = N"(t) N(t) census Eggs laid N'e) = b N(t) Chick survival N"(t) = N'(t)(1- sb) = N (t)b(1- sb) The parameter s here is the strength of the 'Lack' trade-off between offspring number and juvenile survival. A. Write a recursion equation for the number of birds at time t corresponding to the cycle diagram. N°Ct) NH = N'Lt)(I-sb) NtSbl-sb) B. If there at 10 birds in the population at time 0 and the clutch size is 6 = 5 and the strength of the trade-off is s = 0.1, find the numerical solution for N(t) for = {0, 1, ....10}. NCt) NCt tl) = Nt)6(1-sb) N, = 10 (s)(1- (o.1 x5)) = 25 Na = 25(5)(1-(o.1 x5)) = 62.5 No =62.5(5)(1- (0.1 XS)) = 156,25 10 25 2 62.5 %3D 156.25 %3D 390. 625 976.5625 2441.41 6103.52 15258 739 30140,97 1 10 1 95367.4 ナueトの
Transcribed Image Text:IQ2 report all ansuwers to 2 significant digits Student Narme (#): Hui Zhi 301454741 Problem 1: The ornithologist David Lack (1954) proposed that the number of eggs laid per parent, aka the "clutch size", is determined by a trade-off between the number of eggs laid and the survival of the chicks. If the clnteh size is b the cycle diagram for of birds at time 1, N(1), is given by: N(t + 1) = N"(t) N(t) census Eggs laid N'e) = b N(t) Chick survival N"(t) = N'(t)(1- sb) = N (t)b(1- sb) The parameter s here is the strength of the 'Lack' trade-off between offspring number and juvenile survival. A. Write a recursion equation for the number of birds at time t corresponding to the cycle diagram. N°Ct) NH = N'Lt)(I-sb) NtSbl-sb) B. If there at 10 birds in the population at time 0 and the clutch size is 6 = 5 and the strength of the trade-off is s = 0.1, find the numerical solution for N(t) for = {0, 1, ....10}. NCt) NCt tl) = Nt)6(1-sb) N, = 10 (s)(1- (o.1 x5)) = 25 Na = 25(5)(1-(o.1 x5)) = 62.5 No =62.5(5)(1- (0.1 XS)) = 156,25 10 25 2 62.5 %3D 156.25 %3D 390. 625 976.5625 2441.41 6103.52 15258 739 30140,97 1 10 1 95367.4 ナueトの
C. Plot your numerical solution 10D000 1000 1000 00 234 5 6729 10 D. Write the analytical expressions for N(0), N(1), N(2) and N(3). NCO) =NCO) tri =D0 tニ NI)=(NO)b(1-Sb))-sb) N(2)= (NCO)b-sb )²)b(1-sb) = N(0)6-s6?)3 NC3) = LN (bsb)³ )b(I-sb) = NO)(b-sb²)4 N) =(NO)bCl-sb))6(1-sb) = NO)6-sb²)(b-sb²) = NO)(b-sb もti %3D しie2 tt多。 %3D E. What is the general solution of N(t)? What is this type of function called? It is a discrete function NGt) bl-sb) 2
Transcribed Image Text:C. Plot your numerical solution 10D000 1000 1000 00 234 5 6729 10 D. Write the analytical expressions for N(0), N(1), N(2) and N(3). NCO) =NCO) tri =D0 tニ NI)=(NO)b(1-Sb))-sb) N(2)= (NCO)b-sb )²)b(1-sb) = N(0)6-s6?)3 NC3) = LN (bsb)³ )b(I-sb) = NO)(b-sb²)4 N) =(NO)bCl-sb))6(1-sb) = NO)6-sb²)(b-sb²) = NO)(b-sb もti %3D しie2 tt多。 %3D E. What is the general solution of N(t)? What is this type of function called? It is a discrete function NGt) bl-sb) 2
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