7 Scientists observed a colony of seabirds over a period of 10 years starting in 2010.
They concluded that the number of birds in the colony, its population \(P\), could be modelled by a formula of the form
$$P = a \left( 10 ^ { b t } \right)$$
where \(t\) is the time in years after 2010, and \(a\) and \(b\) are constants.
7
- Explain what the value of \(a\) represents.
7 - Show that \(\log _ { 10 } P = b t + \log _ { 10 } a\)
7 - The table below contains some data collected by the scientists.
| Year | 2013 | 2015 |
| \(t\) | 3 | |
| \(P\) | 10200 | 12800 |
| \(\log _ { 10 } P\) | 4.0086 | |
- Complete the table, giving the \(\log _ { 10 } P\) value to 5 significant figures.
7
- (ii) Use the data to calculate the value of \(a\) and the value of \(b\).
7 - (iii) Use the model to estimate the population of the colony in 2024.
7 - State an assumption that must be made in using the model to estimate the population of the colony in 2024.
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[1 mark]
7
- (ii) Hence comment, with a reason, on the reliability of your estimate made in part (c)(iii).
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[1 mark]
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