A population has Leslie matrix L $=$

$$

$$

$$

$$

$0125$

$0\mathrm{.}5000$

$00\mathrm{.}700$

$000\mathrm{.}50$

$$

$$

$$

$$ and $$x $(0)=$

$$

$$

$$

$$

$10$

$10$

$10$

$10$

$$

$$

$$

$$ as the initial population

vector. Compute $$x $(1),$x $(2),$ and $$x $(3)$ exactly and approximate $$x $(50)$ to the nearest integer