Science:Math Exam Resources/Courses/MATH221/December 2019/Question 04 (d)/Statement

In each of the following, indicate the correct answer (and only the correct answer) by circling the appropriate letter. You do not have to show your work in this question.

A population of raccoons has two classes: juveniles and adults. Let the population in year $n$ be given by the vector ${\bf {x}}_{n}={\begin{bmatrix}j_{n}\\a_{n}\end{bmatrix}}$

where $j_{n}$ and $a_{n}$ indicate juveniles and adults at year $n$ respectively.

Wildlife biologists determine that each year, $50\%$ of the juveniles mature to become adults in the following year (the rest die), and $50\%$ of the adults survive to the following year. Additionally, each adult has 2 offspring each year.

Suppose that the raccoon population in 2019 is given by ${\bf {x}}_{2019}={\begin{bmatrix}12\\8\end{bmatrix}}$. Find the population vector for 2017, that is, calculate ${\bf {x}}_{2017}$.

A: $\;{\begin{bmatrix}24\\10\end{bmatrix}}\quad$ B: $\;{\begin{bmatrix}20\\17\end{bmatrix}}\quad$ C: $\;{\begin{bmatrix}10\\6\end{bmatrix}}\quad$ D: $\;{\begin{bmatrix}20\\4\end{bmatrix}}\quad$ E: $\;{\begin{bmatrix}7\\5\end{bmatrix}}$