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 $\surd \left( {2A - 5} \right)$.
a) Write down a differential equation representing the biologist’s claim.
b) 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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