Comparing two exponential models with a second line

A new website records its number of visitors, \(N\), in week \(t\) after its launch. It is believed that \(N=Ab^t\), where \(A\) and \(b\) are constants.

1. Explain why the graph of \(\lg N\) against \(t\) should be a straight line. On the graph paper below, plot \(\lg N\) against \(t\) and draw a straight line of best fit.
2. Use your graph to estimate the value of \(A\) and of \(b\).
3. An older website has \(M=4000(0.8)^t\) visitors in week \(t\). By drawing a suitable straight line on your graph, estimate the value of \(t\) for which the two websites have the same number of visitors. State the equation of the line you draw in terms of \(\lg N\) and \(t\).