Standard +0.8 This is a separable differential equation requiring partial fractions, integration, and solving for t with logarithms. While the technique is standard for Further Maths, the multi-step algebraic manipulation (partial fractions with the specific form, applying initial conditions P(0)=1, then solving for when P=2) and careful handling of constants makes this moderately challenging, above average difficulty but not requiring novel insight.
A population of meerkats is being studied.
The population is modelled by the differential equation
$$\frac{\mathrm{d}P}{\mathrm{d}t} = \frac{1}{22}P(11 - 2P), \quad t \geq 0, \quad 0 < P < 5.5$$
where \(P\), in thousands, is the population of meerkats and \(t\) is the time measured in years since the study began.
Given that there were 1000 meerkats in the population when the study began, determine the time taken, in years, for this population of meerkats to double. [7]
A population of meerkats is being studied.
The population is modelled by the differential equation
$$\frac{\mathrm{d}P}{\mathrm{d}t} = \frac{1}{22}P(11 - 2P), \quad t \geq 0, \quad 0 < P < 5.5$$
where $P$, in thousands, is the population of meerkats and $t$ is the time measured in years since the study began.
Given that there were 1000 meerkats in the population when the study began, determine the time taken, in years, for this population of meerkats to double. [7]
\hfill \mbox{\textit{SPS SPS FM Pure 2023 Q8 [7]}}