Modelling with functionsAQA A-Level Maths: Flashcards

What these 13 flashcards ask

What is a mathematical model?
What are the stages of the modelling cycle?
In C=450+0.2x, what does 0.2 represent?
In N=200\times1.5^t, what does 1.5 represent?
What does the value at t=0 represent?
What is the long-term value of \theta=20+70\times0.9^t?
Give a limitation of an exponential growth model.
Give a limitation of h=1.5+12t-5t^2.
What is the domain of a model?
What is a refinement?
Which function suits a constant rate of change?
Which function suits a repeating tide pattern?
Maximum height predicted by h=1.5+12t-5t^2?

Exam questions on Modelling with functions

The height, $h$ metres, of a ball above the ground $t$ seconds after it is thrown upwards is modelled by $h=1.5+12t-5t^2$ for $t\geq0$ .
Find the maximum height of the ball predicted by the model.2 marks
The number of bacteria, $N$ , in a dish $t$ hours after the start of an experiment is modelled by $N=200\times1.5^t$ .
Explain why the model is unlikely to be valid for large values of $t$ .2 marks
A company models the monthly cost, $C$ pounds, of running a delivery van that travels $x$ miles in a month by $C=450+0.2x$ .
Interpret the numbers $450$ and $0.2$ in the context of the model, and state one limitation of the model.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).