Question

2. Suppose the a species has only two age groups. The eigen-values of the birth-death matrix A have been found to be = 5 and 2 = 2. The corresponding eigen-vectors have been found to be Suppose that initially the age groups are: No = 17 and Ni = 19. (a) determine the size of eachage group as a function of time t; (b) determine the total population (that is, the sum of all age groups) as a function of time t. (c) For each age group, determine what fraction of the total population it constitutes for very large times. That is, for t 00. (d) Expose the fraud! Explain why A, as constructed in class, would be impossible.

Answer 1

3 Ma 2,25: 12 V-30). v-() it's general solution is given by y t = centut q est uz - G= No ; G=N, y@) - test (39) +19 é() ryst] [340est + 1982t 4 / */ 584est + 76ext] given by (a) The size of each group is Y CU = 340 est+19eat y EU = sarest +760 2t

is given by (b) the total population = 4, (+)+ CD) =867 est taset fraction is given by yst 340 est+1992 y[et) sazest+ 76et 340 the 3t = 597 +7683 term calculate t o for laim long yet 3407192 340 lim - Lim go - to 527+76 e 3t = 592 = 20 fraction is 20 : 31 ans