4.04: Linearised exponential relationship

0606/21/M/J/26 — Question 4 · 9 marks

A graph of \(\ln(3y)\) against \(x^2\) is a straight line through \((4.64,12.24)\) and \((6.84,8.94)\).
(a)
Show that \(y=k\mathrm e^{ax^2}\), where \(k\) and \(a\) are exact constants, and find them.
[6]
(b)
Find \(y\) when \(x=3\).
[1]
(c)
Find the possible values of \(x\) when \(y=10\).
[2]