Modelling with functionsAQA A-Level Maths: Mind map

Exam questions on Modelling with functions

1. 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
2. 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
3. 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