IB Maths AI HL AI 5.2 practice question

Paper 2Medium6 marks

A pump transfers liquid into a container. For $t\geq 0$ its flow rate is modelled by

q(t)=2t e^{-t^2}\ \text{L min}^{-1},

where $t$ is the time in minutes since the pump starts. Let $V(t)$ litres be the total volume transferred by time $t$

(a)

Show that $V(t)=1-e^{-t^2}$

[2]

(b)

Calculate the volume transferred in the first $1.5$ minutes. Give your answer to three significant figures.

[1]

(c)

Determine the time at which $0.80$ L has been transferred. Explain why any other mathematical solution is not relevant.

[3]