- The growth of pond weed on the surface of a pond is being investigated.
The surface area of the pond covered by the weed, \(A \mathrm {~m} ^ { 2 }\), can be modelled by the equation
$$A = 0.2 \mathrm { e } ^ { 0.3 t }$$
where \(t\) is the number of days after the start of the investigation.
- State the surface area of the pond covered by the weed at the start of the investigation.
- Find the rate of increase of the surface area of the pond covered by the weed, in \(\mathrm { m } ^ { 2 } /\) day, exactly 5 days after the start of the investigation.
Given that the pond has a surface area of \(100 \mathrm {~m} ^ { 2 }\),
- find, to the nearest hour, the time taken, according to the model, for the surface of the pond to be fully covered by the weed.
The pond is observed for one month and by the end of the month \(90 \%\) of the surface area of the pond was covered by the weed.
- Evaluate the model in light of this information, giving a reason for your answer.