Specialist2025 NHT Exam 1 · Q5Tech-free5 marks

Logistic differential equation for a bee population

The growth of a population of bees is modelled by the logistic differential equation

$\frac{dB}{dt} = 0.03B\left(1 - \frac{B}{500}\right)$ , where is the number of bees after weeks.

Use integration to show that $t = \frac{100}{3}\log_e\left(\frac{3B}{1000 - 2B}\right)$ .

4 marks

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Find the value of $t$ for which the population is increasing most rapidly.

1 mark

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