2020 RVHS P1 Q10

Sales agent \(A\) started work on 1st June 2020. He plans to acquire \(2\) clients in his first month of work and thereafter increase his clientele by \(3\) every month.

1. Find the number of clients agent \(A\) would acquire in June 2021.[2]
2. Find the number of months needed for agent \(A\) to acquire at least \(500\) clients in total.[3]

Sales agent \(B\) has a total \(500\) clients on 1st June 2020. Like agent \(A\), he also acquires \(3\) new clients every month. However, due to strong competition from other sales agents, agent \(B\) loses \(1\%\) of his clientele at the end of each month when the clients choose not to continue with his service from the following month.

3. Show that the clientele size of agent \(B\) at the end of \(n\)th month is given by
   \(297+203{{\left( 0.99 \right)}^{n}}\)[4]
4. The clientele size of agent \(B\) will eventually stabilise. State the value of this clientele size.[1]
5. Agent \(B\) wishes to keep a clientele size of at least \(350\). Find the maximum percentage loss of clients he can have at the end of each month in order to meet this target.[3]