Using the shape of the data in Figure 1, choose a linear or quadratic model for $h$ in terms of $t$ Justify your choice.

Let $h=at^2+bt+c$ Using the measurements at $t=0$ $t=2$ and $t=4$ show that a fitted model is

Hence, using this model, determine the first time during the 5-minute measurement interval at which the model predicts $h=25.0$ cm. Give your answer to the nearest $0.01$ minute.

At $t=3$ compare the model’s predicted height with the recorded height. State what this comparison suggests about the model’s fit at that time.

Use the fitted model to predict the height after 8 minutes. State whether this prediction should be considered reliable, giving two reasons.