Question

is 3 years Suppose a population has the characteristics listed below. (a) A total of 60% of the population survives its first year. Of that 60%, 50% survives the second year. The maximum life (6) The average number of offspring for each member of the population is 4 the first year, 5 the second year, and 4 the third span The population now consists of 150 members in each of the three age class. How many members will be in each age class after one year? year. are the number members in each age class after one year and after two years respectively. a. X2 b. 12 = 90 and >> 75 $1,950 18,5501 90 and x3 = 1,170 75 45 1,950 18,6001 1,050 30 1,350 58,5507 75 and X; 1,170 60 45 52,550 8,550 75 and x3 =1,170 75 75 51,3507 8,600 75 and x3 = 1,050 60 30 = ܕOc1 = ܕܐ ܘ 0 e. I,

Answer 1

The age transition matrix is given by  

$L=\begin{bmatrix} 4& 5&4\\ \frac{60}{100}& 0&0\\ 0& \frac{50}{100}& 0 \end{bmatrix}$

And the age distribution matrix is

$^{x_{1}}=\begin{bmatrix} 150\\ 150\\ 150 \end{bmatrix}$

After 1 year the age transition matrix will be

${x_{2}}=Lx_{1}=\begin{bmatrix} 4& 5&4\\ \frac{60}{100}& 0&0\\ 0& \frac{50}{100}& 0 \end{bmatrix}\begin{bmatrix} 150\\ 150\\ 150 \end{bmatrix}$

  $=\begin{bmatrix} 1950\\ 90\\ 75 \end{bmatrix}$

After 2 year , the age transition matrix will be

${x_{3}}=Lx_{2}=\begin{bmatrix} 4& 5&4\\ \frac{3}{5}& 0&0\\ 0& \frac{1}{2}& 0 \end{bmatrix}\begin{bmatrix} 1950\\ 90\\ 75 \end{bmatrix}$

  $=\begin{bmatrix} 8550\\ 1170\\ 45 \end{bmatrix}$

Hence the answer is option (a)