12 Answer part (ii) of this question on the insert provided.
Since 1945 the populations of many countries have been growing. The table shows the estimated population of 15- to 59-year-olds in Africa during the period 1955 to 2005.
| Year | 1955 | 1965 | 1975 | 1985 | 1995 | 2005 |
| Population (millions) | 131 | 161 | 209 | 277 | 372 | 492 |
Source: United Nations
Such estimates are used to model future population growth and world needs of resources. One model is \(P = a 10 ^ { b t }\), where the population is \(P\) millions, \(t\) is the number of years after 1945 and \(a\) and \(b\) are constants.
- Show that, using this model, the graph of \(\log _ { 10 } P\) against \(t\) is a straight line of gradient \(b\). State the intercept of this line on the vertical axis.
- On the insert, complete the table, giving values correct to 2 decimal places, and plot the graph of \(\log _ { 10 } P\) against \(t\). Draw, by eye, a line of best fit on your graph.
- Use your graph to find the equation for \(P\) in terms of \(t\).
- Use your results to estimate the population of 15- to 59-year-olds in Africa in 2050. Comment, with a reason, on the reliability of this estimate.