2024 IGCSE Additional Mathematics May/June 0606/22 Q8

An experiment was carried out and values of \(y\) for certain values of \(x\) were recorded. The table shows the values recorded.

The relationship between \(y\) and \(x\) is modelled by \(y=A\mathrm{e}^{kx}\), where \(A\) and \(k\) are constants.

1. Draw a straight line graph for \(\ln y\) against \(x\).[2]
2. Find the equation of the line in part (a) and hence find the values of \(A\) and \(k\). Give each value correct to \(1\) significant figure.[5]
3. Find the value of \(x\) for which \(y=17\).[2]