2.5 Modelling with functionsIB Maths: Applications and Interpretation HL: Mind map

Exam questions on 2.5 Modelling with functions

1. A mobile phone plan costs 45 AED per month and includes 5 GB of data. Each extra GB used beyond 5 GB costs 8 AED. The monthly cost is $C$ AED when $d$ GB are used, $d\geq 0$.
   Write down the gradient of the model for $d>5$ and interpret it in context.2 marks
2. A footballer kicks a ball from the ground. Its height $h$ metres, when it has travelled a horizontal distance $x$ metres, is modelled by $h(x)=-0.04x^2+0.96x$, for $x\geq 0$ while the ball is in the air.
   Use your GDC to find the horizontal distance at which the ball is at a height of 5 m on its way up.2 marks
3. A cup of coffee is poured at $t=0$ minutes in a room. Its temperature $T$ °C is modelled by $T(t)=22+68e^{-0.05t}$, for $t\geq 0$.
   (i) Find the temperature of the coffee when it is poured. (ii) Write down the equation of the horizontal asymptote of the graph of $T$ and interpret it in context.3 marks