SPS SPS SM Pure 2022 June — Question 16

Exam BoardSPS
ModuleSPS SM Pure (SPS SM Pure)
Year2022
SessionJune
TopicExponential Equations & Modelling

16. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{8053bd07-c2b2-4ada-ae0e-8ab6b8466c78-34_606_737_146_760} \captionsetup{labelformat=empty} \caption{Figure 6
In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable.}
\end{figure} Figure 6 shows a sketch of part of the curve with equation $$y = 3 \times 2 ^ { 2 x } .$$ The point \(P ( a , 96 \sqrt { } 2 )\) lies on the curve.
  1. Find the exact value of \(a\). The curve with equation \(y = 3 \times 2 ^ { 2 x }\) meets the curve with equation \(y = 6 ^ { 3 - x }\) at the point \(Q\).
  2. Show that the \(x\) coordinate of \(Q\) is \(\frac { 3 + 2 \log _ { 2 } 3 } { 3 + \log _ { 2 } 3 }\).
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