SPS SPS SM 2020 June — Question 12

Exam BoardSPS
ModuleSPS SM (SPS SM)
Year2020
SessionJune
TopicExponential Equations & Modelling

12. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{f2033889-3cc5-48de-9bdb-cb1861921a2a-11_572_675_1098_772} \captionsetup{labelformat=empty} \caption{Figure 6}
\end{figure} \section*{In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable.} 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 $$\frac { 3 + 2 \log _ { 2 } 3 } { 3 + \log _ { 2 } 3 }$$