5.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{76205772-5395-4ab2-96f9-ad9803b8388c-16_582_737_248_607}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
The growth of duckweed on a pond is being studied.
The surface area of the pond covered by duckweed, \(A \mathrm {~m} ^ { 2 }\), at a time \(t\) days after the start of the study is modelled by the equation
$$A = p q ^ { t } \quad \text { where } p \text { and } q \text { are positive constants }$$
Figure 1 shows the linear relationship between \(\log _ { 10 } A\) and \(t\).
The points \(( 0,0.32 )\) and \(( 8,0.56 )\) lie on the line as shown.
- Find, to 3 decimal places, the value of \(p\) and the value of \(q\).
Using the model with the values of \(p\) and \(q\) found in part (a),
- find the rate of increase of the surface area of the pond covered by duckweed, in \(\mathrm { m } ^ { 2 }\) / day, exactly 6 days after the start of the study.
Give your answer to 2 decimal places.
\includegraphics[max width=\textwidth, alt={}, center]{76205772-5395-4ab2-96f9-ad9803b8388c-19_2649_1840_117_114}