CAIE P2 2020 June — Question 4

Exam BoardCAIE
ModuleP2 (Pure Mathematics 2)
Year2020
SessionJune
TopicCurve Sketching
TypeLogarithmic graph for power law

4
\includegraphics[max width=\textwidth, alt={}, center]{01f2de2b-3482-4694-889e-7fcd016b57e3-06_659_828_262_660} The variables \(x\) and \(y\) satisfy the equation \(y = A x ^ { - 2 p }\), where \(A\) and \(p\) are constants. The graph of \(\ln y\) against \(\ln x\) is a straight line passing through the points \(( - 0.68,3.02 )\) and \(( 1.07 , - 1.53 )\), as shown in the diagram. Find the values of \(A\) and \(p\).