Modelling with functionsEdexcel A-Level Maths: Mind map

Exam questions on Modelling with functions

1. 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
2. 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
3. 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