- A scientist monitored the growth of bacteria on a dish over a 30 -day period.
The area, \(N \mathrm {~mm} ^ { 2 }\), of the dish covered by bacteria, \(t\) days after monitoring began, is modelled by the equation
$$\log _ { 10 } N = 0.0646 t + 1.478 \quad 0 \leqslant t \leqslant 30$$
- Show that this equation may be written in the form
$$N = a b ^ { t }$$
where \(a\) and \(b\) are constants to be found. Give the value of \(a\) to the nearest integer and give the value of \(b\) to 3 significant figures.
- Use the model to find the area of the dish covered by bacteria 30 days after monitoring began. Give your answer, in \(\mathrm { mm } ^ { 2 }\), to 2 significant figures.