CAIE P3 2024 June — Question 3

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2024
SessionJune
TopicExponential Equations & Modelling

3
\includegraphics[max width=\textwidth, alt={}, center]{37f00894-e6b1-4961-bd3c-4852e43173d0-04_597_921_260_573} The variables \(x\) and \(y\) satisfy the equation \(\mathrm { a } ^ { \mathrm { y } } = \mathrm { bx }\), where \(a\) and \(b\) are constants. The graph of \(y\) against \(\ln x\) is a straight line passing through the points ( \(0.336,1.00\) ) and ( \(1.31,1.50\) ), as shown in the diagram. Find the values of \(a\) and \(b\). Give each value correct to the nearest integer.