Question

help me with this calculus question please!!

For the following Leslie matrix, (a) find a population of size 40,000 for which the proportion of the population in each age group stays the same from one year to the next, and (b) tell by what factor the population grows or declines each year 0.2 1.4 0.3 0.1 (a) Let the first and second columns of the Leslie matrix correspond to the populations x1 and x2, respectively. The population in each age group stays the same from one year to the next if Type an integer or decimal for each matrix element.)

Answer 1

Given matrix: - [0.2 0.3 1.4 0.1] Since, the population is each age group stays the same from one year to the next i.e., 40,000. so, [0.2, 0.3 1.4 0.1] [x_1 x_2] [x_1 x_2] = [40 000 40 000] that implies, 0.2x_1 + 1.4x_2 = 40 000 (1) & 0.3 x_1 + 0.1 x_2 = 40000 (2) From (1) & (2) 0.2x_1 + 1.4x_2 = 0.3x_1 + 0.1x_2 1.3x_2 = 0.1x_1 13x_2 = x_1 put x_1 = 13 x_2 in (1) 0.2 (13x_2) + 1.4 x_2 = 40 000 2.6 x_2 1.4 x_2 = 40 000 4x_2 = 40 000 x_2 10 000 so, x_1 = 13 x_2 = 130000 so, [x_1 x_2] = [10 000 13 0000]