12 The table shows the size of a population of house sparrows from 1980 to 2005.
| Year | 1980 | 1985 | 1990 | 1995 | 2000 | 2005 |
| Population | 25000 | 22000 | 18750 | 16250 | 13500 | 12000 |
The 'red alert' category for birds is used when a population has decreased by at least \(50 \%\) in the previous 25 years.
- Show that the information for this population is consistent with the house sparrow being on red alert in 2005.
The size of the population may be modelled by a function of the form \(P = a \times 10 ^ { - k t }\), where \(P\) is the population, \(t\) is the number of years after 1980, and \(a\) and \(k\) are constants.
- Write the equation \(P = a \times 10 ^ { - k t }\) in logarithmic form using base 10, giving your answer as simply as possible.
- Complete the table and draw the graph of \(\log _ { 10 } P\) against \(t\), drawing a line of best fit by eye.
- Use your graph to find the values of \(a\) and \(k\) and hence the equation for \(P\) in terms of \(t\).
- Find the size of the population in 2015 as predicted by this model.
Would the house sparrow still be on red alert? Give a reason for your answer.