IB Maths AI HL Sl 2 5 Modelling with Functions Topic Practice

This question explores models for the height of water in a cylindrical container as water drains out.
The diagram shows a cylindrical water container of height 3.2 metres and base radius 1 metre. At the base of the container is a small circular valve, which enables water to drain out.

Eva closes the valve and fills the container with water.
At time t=0, Eva opens the valve. She records the height, h metres, of water remaining in the container every 5 minutes.

Eva first tries to model the height using a linear function, h(t)=a t+b, where $a, b \in \mathbb{R}$.

Interpret the meaning of parameter a in the context of the model.

Eva uses the equation of the regression line of h on t, to predict the time it will take for all the water to drain out of the container.