<p>In the controlled environment of Laboratory (Lab) $A$ where cells are cultivated, the number of cells increases by $250\%$ from the start of the week to the end of the week. At the end of each week, $1.2$ million cells are transferred to another laboratory for experiments. The number of cells (in millions) in Lab $A$ at the start of the ${{n}^{\mathrm{th}}}$ week is given by ${{a}_{n}}$.</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Show that ${{a}_{n}}={{3.5}^{n-1}}{{a}_{1}}-0.48\left( {{3.5}^{n-1}}-1 \right)$.</span></div><p style="text-align: right;">[3]</p></li></ol>
<p>It is given that Lab $A$ begins operating at the start of the first week with $0.5$ million cells.</p>
<ol class="i-list" start="2"><li><div class="list-item-content"><span class="list-item-text">Find the number of cells in Lab $A$ at the end of the third week, before the cells are transferred to another laboratory.</span></div><p style="text-align: right;">[2]</p></li></ol>
<p>A research requires at least $60$ million cells before it can commence. To facilitate this, Lab $A$ and Lab $B$ are to cultivate and combine all the cells in both the labs by the start of a certain week. Lab B begins operating one week after Lab $A$.</p>
<p>Lab $B$ begins operating at the start of that week with $0.5$ million cells and cultivates $5$ million cells by the end of that week. At the end of each subsequent week, Lab $B$ cultivates $5$ million cells more than in the previous week.</p>
<ol class="i-list" start="3"><li><div class="list-item-content"><span class="list-item-text">In which week can the research first commence?</span></div><p style="text-align: right;">[3]</p></li></ol>

In the controlled environment of Laboratory (Lab) $A$ where cells are cultivated, the number of cells increases by $250\%$ from the start of the week to the end of the week. At the end of each week, $1.2$ million cells are transferred to another laboratory for experiments. The number of cells (in millions) in Lab $A$ at the start of the ${{n}^{\mathrm{th}}}$ week is given by ${{a}_{n}}$.

Show that ${{a}_{n}}={{3.5}^{n-1}}{{a}_{1}}-0.48\left( {{3.5}^{n-1}}-1 \right)$.

It is given that Lab $A$ begins operating at the start of the first week with $0.5$ million cells.

Find the number of cells in Lab $A$ at the end of the third week, before the cells are transferred to another laboratory.

A research requires at least $60$ million cells before it can commence. To facilitate this, Lab $A$ and Lab $B$ are to cultivate and combine all the cells in both the labs by the start of a certain week. Lab B begins operating one week after Lab $A$.

Lab $B$ begins operating at the start of that week with $0.5$ million cells and cultivates $5$ million cells by the end of that week. At the end of each subsequent week, Lab $B$ cultivates $5$ million cells more than in the previous week.

2020 NJC P2 Q3

2020 NJC P2 Q3

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