2022 VJC Promo Q11
In a laboratory experiment, a tank is transported to and fro between station $A$ and station $B$.
On the ${{1}^{\text{st}}}$ visit to station $A$, $200$ ml of water is added into the tank and on subsequent visits, $200$ ml more water than the previous visit to station $A$ will be added. That is, $400$ ml and $600$ ml of water will be added into the tank on the ${{2}^{\text{nd}}}$ and ${{3}^{\text{rd}}}$ visit to station $A$ respectively. On each visit to station $B$, $b$ ml of water is removed from the tank.
It is given that the tank is empty at the start of the experiment and it starts from station $A$.
(i)
On the$~{{m}^{\text{th}}}$ visit to station $A$, $3200$ml of water is added into the tank. Find $m$.
[2]
(ii)
It is given that immediately after the ${{16}^{\text{th}}}$ visit to station $B$, there is more than $25$ litres of water in the tank. Find the set of values that $b$ can take.
[3]
In another laboratory experiment, a tank is transported to and fro between station $A$ and station $C$. $10%$ of the water in the tank is removed on each visit to station $C$. It is given that the tank is empty at the start of the experiment and it starts from station $A$.
(iii)
Show that the amount of water in the tank immediately after the ${{3}^{\text{rd}}}$ visit to station $C$ is $1009.8$ ml.
[2]
(iv)
Show that the amount of water in the tank immediately after the ${{n}^{\text{th}}}$ visit to station $C$ is $1800n-16\,200\left( 1-{{0.9}^{n}} \right)$.
[4]
(v)
The experiment stops when the amount of water in the tank immediately after it leaves station $C$ exceeds $10$ litres. After the ${{k}^{\text{th}}}$ visit to station $C$, the experiment stopped. Find $k$.
[1]
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