Mathematical modellingAQA A-Level Maths: Mind map

Exam questions on Mathematical modelling

1. A ball is thrown upwards from a height of 1.5 m. Its height $h$ metres after $t$ seconds is modelled by $h=1.5+12t-5t^2$ for $t\ge0$.
   The model is only valid for part of the ball's flight. Find the range of values of $t$ for which it is valid, giving your reasoning.2 marks
2. A population of bacteria is modelled by $P=200\times1.5^t$, where $P$ is the number of bacteria and $t$ is the time in hours after the start of an experiment.
   The model predicts about $665\,000$ bacteria after 20 hours, but in the experiment the population levels off at about 5000. Explain why the model fails, and suggest a refinement.2 marks
3. A van hire company's cost model is $C=40+25d$, where $C$ is the cost in pounds and $d$ is the number of days of hire.
   Interpret the numbers $40$ and $25$ in the model, and state one assumption it makes.3 marks