12 The table shows population data for a country.
| Year | 1969 | 1979 | 1989 | 1999 | 2009 |
| Population in | | millions \(( p )\) |
| 58.81 | 80.35 | 105.27 | 134.79 | 169.71 |
The data may be represented by an exponential model of growth. Using \(t\) as the number of years after 1960, a suitable model is \(p = a \times 10 ^ { k t }\).
- Derive an equation for \(\log _ { 10 } p\) in terms of \(a , k\) and \(t\).
- Complete the table and draw the graph of \(\log _ { 10 } p\) against \(t\), drawing a line of best fit by eye.
- Use your line of best fit to express \(\log _ { 10 } p\) in terms of \(t\) and hence find \(p\) in terms of \(t\).
- According to the model, what was the population in 1960 ?
- According to the model, when will the population reach 200 million?