- An area of sea floor is being monitored.
The area of the sea floor, \(S \mathrm {~km} ^ { 2 }\), covered by coral reefs is modelled by the equation
$$S = p q ^ { t }$$
where \(p\) and \(q\) are constants and \(t\) is the number of years after monitoring began.
Given that
$$\log _ { 10 } S = 4.5 - 0.006 t$$
- find, according to the model, the area of sea floor covered by coral reefs when \(t = 2\)
- find a complete equation for the model in the form
$$S = p q ^ { t }$$
giving the value of \(p\) and the value of \(q\) each to 3 significant figures.
- With reference to the model, interpret the value of the constant \(q\)