Moderate -0.3 This is a standard logarithmic transformation question requiring students to recognize that ln(y) = ln(a) + x·ln(b) gives a linear relationship, then use two points to find the gradient and intercept. The arithmetic is straightforward with no conceptual challenges beyond the core technique, making it slightly easier than average.
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\includegraphics[max width=\textwidth, alt={}, center]{72d50061-ead5-466a-96fc-2203438d1407-2_654_693_532_724}
The variables \(x\) and \(y\) satisfy the equation \(y = a \left( b ^ { x } \right)\), where \(a\) and \(b\) are constants. The graph of \(\ln y\) against \(x\) is a straight line passing through the points ( \(0.75,1.70\) ) and ( \(1.53,2.18\) ), as shown in the diagram. Find the values of \(a\) and \(b\) correct to 2 decimal places.
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\includegraphics[max width=\textwidth, alt={}, center]{72d50061-ead5-466a-96fc-2203438d1407-2_654_693_532_724}
The variables $x$ and $y$ satisfy the equation $y = a \left( b ^ { x } \right)$, where $a$ and $b$ are constants. The graph of $\ln y$ against $x$ is a straight line passing through the points ( $0.75,1.70$ ) and ( $1.53,2.18$ ), as shown in the diagram. Find the values of $a$ and $b$ correct to 2 decimal places.
\hfill \mbox{\textit{CAIE P2 2014 Q2 [5]}}