Standard +0.3 This is a standard logarithmic linearization problem requiring students to take ln of both sides to get ln(y) = ln(K) + px·ln(2), identify gradient and intercept from two points, then solve for K and p. It's slightly easier than average as it's a routine textbook exercise with clear steps: find gradient, find intercept, apply exponential/logarithm rules. The calculation is straightforward with no conceptual surprises.
5
\includegraphics[max width=\textwidth, alt={}, center]{22ba6cc7-7375-434e-9eaa-d536684dd727-2_583_597_1457_772}
The variables \(x\) and \(y\) satisfy the equation \(y = K \left( 2 ^ { p x } \right)\), where \(K\) and \(p\) are constants. The graph of \(\ln y\) against \(x\) is a straight line passing through the points ( \(1.35,1.87\) ) and ( \(3.35,3.81\) ), as shown in the diagram. Find the values of \(K\) and \(p\) correct to 2 decimal places. [0pt]
[6]
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\includegraphics[max width=\textwidth, alt={}, center]{22ba6cc7-7375-434e-9eaa-d536684dd727-2_583_597_1457_772}
The variables $x$ and $y$ satisfy the equation $y = K \left( 2 ^ { p x } \right)$, where $K$ and $p$ are constants. The graph of $\ln y$ against $x$ is a straight line passing through the points ( $1.35,1.87$ ) and ( $3.35,3.81$ ), as shown in the diagram. Find the values of $K$ and $p$ correct to 2 decimal places.\\[0pt]
[6]
\hfill \mbox{\textit{CAIE P2 2014 Q5 [6]}}