Modelling with functionsEdexcel A-Level Maths: Flashcards

What these 12 flashcards ask

Which function models exponential growth?
What does T=a+be^{-kt} predict as t\to\infty?
What are the mean, amplitude and period of d=a+b\sin(ct)^\circ?
Which function models inverse proportion?
How do you find k in P=\frac kV?
First step to solve 50=20+70e^{-0.05t}?
For N=500e^{0.4t}, what is \frac{dN}{dt}?
Main limitation of unlimited exponential growth?
What is the long-term value of N=\frac{20000}{1+39e^{-0.4t}}?
Maximum and minimum of d=6+2.5\sin(30t)^\circ?
Why can a gas pressure model P=\frac kV fail?
How do you calculate percentage error of a prediction?

Exam questions on Modelling with functions

The temperature, $T\,^\circ\text{C}$ , of a cup of tea $t$ minutes after it is made is modelled by $T=20+70e^{-0.05t}$ , $t\geq0$ .
Find the time taken for the tea to cool to $50\,^\circ\text{C}$ , giving your answer to $3$ significant figures.2 marks
The depth of water, $d$ metres, in a harbour $t$ hours after midnight is modelled by $d=6+2.5\sin(30t)^\circ$ , $0\leq t\leq24$ .
Find the first time after midnight at which the depth is $4.75$ m, giving your answer as a time of day.2 marks
The pressure, $P$ kPa, of a fixed mass of gas at constant temperature is modelled as inversely proportional to its volume, $V\,\text{cm}^3$ . When $V=250$ , $P=120$ .
Show that $P=\frac{30000}{V}$ and use the model to find the pressure when $V=80$ .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).