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.
(i)
Find the number of clients agent $A$ would acquire in June 2021.
[2]
(ii)
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.
(iii)
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]
(iv)
The clientele size of agent $B$ will eventually stabilise. State the value of this clientele size.
[1]
(v)
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]
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