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Year 12 Specialist (Unit 3 & 4) Rates of change and differential equations

The logistic differential equation

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Questions
Question 1
163356

A population of bacteria grows according to the differential equation:
\[
\frac{d P}{d t}=0.04 P(1-0.002 P), P_0=100,0<P<500
\]
Find the population \(P\) at time \(t\).

\(P=\dfrac{500 e^{0.04 t}}{4+e^{0.04 t}}\)

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