Standard +0.8 This is a separable differential equation requiring partial fractions, integration, and solving for t when P doubles. While the setup is standard Further Maths material, the multi-step algebraic manipulation (partial fractions of 1/[P(11-2P)], applying limits, solving the resulting logarithmic equation) and careful handling of the initial condition P(0)=1 to find P(t)=2 makes this moderately challenging, above average difficulty but not exceptionally hard for FM students.
A population of meerkats is being studied.
The population is modelled by the differential equation
$$\frac{dP}{dt} = \frac{1}{22}P(11 - 2P), \quad t \geq 0, \quad 0 < P < 5.5$$
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
$$\frac{dP}{dt} = \frac{1}{22}P(11 - 2P), \quad t \geq 0, \quad 0 < P < 5.5$$
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 2025 Q8 [7]}}