- The world human population, \(P\) billions, is modelled by the equation
$$P = a b ^ { t }$$
where \(a\) and \(b\) are constants and \(t\) is the number of years after 2004
Using the estimated population figures for the years from 2004 to 2007, a graph is plotted of \(\log _ { 10 } P\) against \(t\).
The points lie approximately on a straight line with
- gradient 0.0054
- intercept 0.81 on the \(\log _ { 10 } P\) axis
- Estimate, to 3 decimal places, the value of \(a\) and the value of \(b\).
In the context of the model,
- interpret the value of the constant \(a\),
- interpret the value of the constant \(b\).
Use the model to estimate the world human population in 2030Comment on the reliability of the answer to part (c).