CAIE P2 2022 March — Question 3

Exam BoardCAIE
ModuleP2 (Pure Mathematics 2)
Year2022
SessionMarch
TopicExponential Equations & Modelling

3 The variables \(x\) and \(y\) satisfy the equation \(y = 3 ^ { 2 a } a ^ { x }\), where \(a\) is a constant. The graph of \(\ln y\) against \(x\) is a straight line with gradient 0.239 .
  1. Find the value of \(a\) correct to 3 significant figures.
  2. Hence find the value of \(x\) when \(y = 36\). Give your answer correct to 3 significant figures.