Suppose there are two voting parties: A and $B.$ Members of these parties may choose to switch parties at

the end of each year. The following trend has been noted about how often members switch parties:

Each year, $70\%$ of members in party A switch to party $B,$ and the remaining $30\%$ do not switch.

Each year, $65\%$ of members in party $B$ switch to party $A,$ and the remaining $35\%$ do not switch.

Suppose that this year party A has $480$ members and party $B$ has $110$ members.

How many members will be in each party after $1$ year? $[$Round your answer to the nearest whole number.$]$

In party $A$:

In party $B$ :

How many members will be in each party after $4$ years? $[$Round your answer to the nearest whole number.$]$

In party $A$ :

In party $B$ :

If the vector $\left[\begin{array}{c}a\\ b\end{array}\right]$ represents the distribution of people in party A and party $B,$ write the matrix that will

transform this vector to show the distribution after $1$ year.

Answer:

$\left[\begin{array}{c}\\ \end{array}\right]$