Constructing differential equationsEdexcel A-Level Maths: Flashcards

What these 12 flashcards ask

'The rate of increase of N is proportional to N' as an equation?
'The rate of decrease of N is proportional to N'?
'Inversely proportional to r^{2}' (rate of change of r)?
What does 'rate of change with respect to time' mean in symbols?
How do you find k in a constructed model?
Net rate for inflow and outflow?
What is an equilibrium?
Tank: V=2h, so what is \frac{dV}{dt}?
Drug: drip 5 mg per hour, removal kx. Differential equation?
Kinematics: acceleration proportional to velocity, opposing motion?
Price and demand: D falls in proportion to D as p rises?
Does this topic require you to solve the equation?

Exam questions on Constructing differential equations

A population of insects has $N$ individuals at time $t$ days. The rate of increase of $N$ is proportional to $N$ . Initially $N=500$ and the population is increasing at $60$ insects per day.
Find the rate of increase of the population when $N=2000$ .2 marks
A spherical ball of ice melts so that its radius $r$ cm decreases at a rate that is inversely proportional to the square of the radius. Time $t$ is measured in minutes. When $r=2$ , the radius is decreasing at $0.1$ cm per minute.
Find the rate at which the radius is decreasing when $r=0.5$ .2 marks
Water flows into a tank at a constant rate of $0.6$ m $^3$ per minute and leaves through a hole in the base at a rate of $0.1\sqrt h$ m $^3$ per minute, where $h$ m is the depth of the water at time $t$ minutes. The tank has a horizontal cross-section of area $2$ m $^2$ , so the volume of water in the tank is $V=2h$ m $^3$ .
Show that $\frac{dh}{dt}=0.3-0.05\sqrt h$ .3 marks

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).