A population has the following characteristics. (a) A total of 75% of the population survives the first year. Of that 75%, 25% survives the

Question

A population has the following characteristics. (a) A total of 75% of the population survives the first year. Of that 75%, 25% survives the second year. The maximum life span is 3 years. (b) The average number of offspring for each member of the population is 3 the first year, 6 the second year, and 3 the third year. The population now consists of 112 members in each of the three age classes. How many members will there be in each age class in 1 year?

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Nevaeh 1 week 2021-09-15T07:43:23+00:00 1 Answer 0

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    2021-09-15T07:44:28+00:00

    Answer:

    = \left[\begin{array}{ccc}1344\\84\\28\end{array}\right]  \left \begin{array}{ccc}{0 \  \leq  age   \leq  1 }\\{ 1 \  \leq  age   \leq  2 }\\{2 \  \leq  age  \leq 3}\end{array}\right

    i.e after the first year ;

    there 1344 members in the first age class

    84 members for the second age class; and

    28 members for the third age class

    Step-by-step explanation:

    We can deduce that the age distribution vector x represents the number of population members for each age class; Given that in each class of age there are 112 members present.

    The current age distribution vector is as follows:

    x = \left[\begin{array}{ccc}1&1&2\\1&1&2\\1&1&2\end{array}\right] \left[\begin{array}{ccc}{0 \  \leq  age   \leq  1 }\\{ 0 \  \leq  age   \leq  2 }\\{0 \  \leq  age   \leq 3}\end{array}\right]

    Also , the age transition matrix is as follows:

    L = \left[\begin{array}{ccc}3&6&3\\0.75&0&0 \\0&0.25&0\end{array}\right]

    After 1 year ; the age distribution vector will be :

    x_2 =Lx_1 = \left[\begin{array}{ccc}3&6&3\\0.75&0&0 \\0&0.25&0\end{array}\right]  \left[\begin{array}{ccc}1&1&2\\1&1&2\\1&1&2\end{array}\right]

    = \left[\begin{array}{ccc}1344\\84\\28\end{array}\right]  \left \begin{array}{ccc}{0 \  \leq  age   \leq 1 }\\{ 1 \  \leq  age   \leq  2 }\\{2 \  \leq  age   \leq  3}\end{array}\right

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45:7+7-4:2-5:5*4+35:2 =? ( )