Moderate -0.3 This is a standard logarithmic transformation question requiring students to convert the exponential equation to linear form (ln y = ln K - 2x ln a), find the gradient and intercept from two points, then solve for K and a. While it involves multiple steps (finding gradient, using point-slope, exponentiating), these are routine techniques practiced extensively in P2 with no novel problem-solving required.
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The variables \(x\) and \(y\) satisfy the equation \(y = \frac { K } { a ^ { 2 x } }\), where \(K\) and \(a\) are constants. The graph of \(\ln y\) against \(x\) is a straight line passing through the points \(( 0.6,1.81 )\) and \(( 1.4,1.39 )\), as shown in the diagram. Find the values of \(K\) and \(a\) correct to 2 significant figures.
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\includegraphics[max width=\textwidth, alt={}, center]{de2f8bf3-fd03-4199-9eb2-c9cbac4d4385-05_551_535_260_806}
The variables $x$ and $y$ satisfy the equation $y = \frac { K } { a ^ { 2 x } }$, where $K$ and $a$ are constants. The graph of $\ln y$ against $x$ is a straight line passing through the points $( 0.6,1.81 )$ and $( 1.4,1.39 )$, as shown in the diagram. Find the values of $K$ and $a$ correct to 2 significant figures.\\
\hfill \mbox{\textit{CAIE P2 2017 Q5 [6]}}