Moderate -0.5 This is a standard textbook exercise on exponential models and logarithmic linearization. Students take ln of both sides to get ln(y) = ln(a) + x·ln(b), recognize this as a linear relationship, find the gradient to get ln(b), then use a point to find ln(a). It requires multiple steps but follows a well-practiced procedure with no novel insight needed—slightly easier than average due to its routine nature.
3
\includegraphics[max width=\textwidth, alt={}, center]{ce3c4a9c-bf83-4d28-96e2-ef31c3673dea-04_860_451_264_833}
The variables \(x\) and \(y\) are related by the equation \(y = a b ^ { x }\), where \(a\) and \(b\) are constants. The diagram shows the result of plotting \(\ln y\) against \(x\) for two pairs of values of \(x\) and \(y\). The coordinates of these points are \(( 1,3.7 )\) and \(( 2.2,6.46 )\).
Use this information to find the values of \(a\) and \(b\).
3\\
\includegraphics[max width=\textwidth, alt={}, center]{ce3c4a9c-bf83-4d28-96e2-ef31c3673dea-04_860_451_264_833}
The variables $x$ and $y$ are related by the equation $y = a b ^ { x }$, where $a$ and $b$ are constants. The diagram shows the result of plotting $\ln y$ against $x$ for two pairs of values of $x$ and $y$. The coordinates of these points are $( 1,3.7 )$ and $( 2.2,6.46 )$.
Use this information to find the values of $a$ and $b$.\\
\hfill \mbox{\textit{CAIE P3 2023 Q3 [4]}}