Science:Math Exam Resources/Courses/MATH221/December 2019/Question 09 (a)/Statement

There are two cities, Delta and Surrey. Every year

• $10\%$ of the population of Delta migrates to Surrey,
• $20\%$ of the population of Surrey migrates to Delta.

Assume there are no other changes to the population of Delta or Surrey. In 2019 it was estimated that the population of Delta was 100,000 people, and that of Surrey was 500,000 people. Let $d_{n}$ and $s_{n}$ respectively denote the population of Delta and Surrey $n$ years from now.

Write down a matrix $A$ such that

$${\begin{bmatrix}d_{n}\\s_{n}\end{bmatrix}}=A{\begin{bmatrix}d_{n-1}\\s_{n-1}.\end{bmatrix}}$$