The table shows values of the variables \(t\) and \(P\).

(i) Draw the graph of \(\ln P\) against \(t\) on the grid below.

(ii) Use the graph to estimate the value of \(P\) when \(t=2.2\).

(iii) Find the gradient of the graph and state the coordinates of the point where the graph meets the vertical axis.

(iv) Using your answers to part (iii), show that \(P=ab^t\), where \(a\) and \(b\) are constants to be found.

(v) Given that your equation in part (iv) is valid for values of \(t\) up to \(10\), find the smallest value of \(t\), correct to 1 decimal place, for which \(P\) is at least \(1000\).