2026 CCHY P2 Q12

A mathematics teacher designed an assessment consisting of \(x\) questions. The average time taken (\(y\) mins) by students is related to the number of questions by \(ae^{2y}=e^{bx^2+4}\), where \(a\) and \(b\) are constants. The table below shows the relationship between \(x\) and \(y\).

1. On the grid below, plot \(2y\) against \(x^2\) and draw a straight-line graph.[2]

2. Use your graph to estimate the value of \(a\) and of \(b\).[3]
3. Use your graph to estimate the value of \(x\) when \(e^y=850\).[2]
4. A student claims that there is a value of \(x\) when \(e^y=0.5\). Explain why the student's claim is impossible.[1]