The table below shows experimental values of two variables \(x\) and \(y\).
| \(x\) | 1 | 2 | 3 | 4 | 5 | 6 |
| \(y\) | 2.20 | 1.74 | 1.71 | 1.83 | 1.87 | 1.96 |
The variables \(x\) and \(y\) are related by the equation \(\dfrac{y}{a}=\dfrac{1}{x}+b\sqrt{x}\), where \(a\) and \(b\) are constants.
One value of \(y\) has been recorded incorrectly.
Show how \(\dfrac{y}{a}=\dfrac{1}{x}+b\sqrt{x}\) is transformed to plot a graph of \(xy\) against \(x\sqrt{x}\).[1]
On the grid provided below, draw a straight line graph of \(xy\) against \(x\sqrt{x}\) for the given data.[2]
Using your graph,
find an approximate value of \(y\) to replace the incorrect value,[2]
estimate the value of \(a\) and of \(b\),[3]
find the value of \(y\) when \(x=2.52\).[2]
A pair of values of \(x\) and \(y\) is considered acceptable only if the \(xy\) value is within \(2\%\) vertical difference from the straight line. A student recorded a pair of values such that \(x=4.50\) and \(y=1.86\). Verify whether the recorded values by the student are acceptable.[2]