Exam-Style Problem
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Nov 2010 p33 q9
2306
A biologist is investigating the spread of a weed in a particular region. At time \(t\) weeks after the start of the investigation, the area covered by the weed is \(A \text{ m}^2\). The biologist claims that the rate of increase of \(A\) is proportional to \(\sqrt{2A - 5}\).
(i) Write down a differential equation representing the biologist’s claim.
(ii) At the start of the investigation, the area covered by the weed was \(7 \text{ m}^2\) and, 10 weeks later, the area covered was \(27 \text{ m}^2\). Assuming that the biologist’s claim is correct, find the area covered 20 weeks after the start of the investigation.
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