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1.10.8 Numerical methods to solve problems (A-level only)

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Question 4

A scientist is monitoring the volume of a gas in a controlled chamber.

Exactly 2 minutes after the start of the experiment, the volume of the gas was 3 m33\text{ m}^33 m3.

Exactly 4 minutes after the start of the experiment, the volume of the gas was 4 m34\text{ m}^34 m3.

Given that the volume, V m3V\text{ m}^3V m3, of the gas, ttt minutes after the start of the experiment, can be modelled by the equation

V2=pt2+q V^2 = pt^2 + q V2=pt2+q

where ppp and qqq are constants,

a.

find, to 3 significant figures where necessary, the value of ppp and the value of qqq.

[4]
b.

Exactly TTT minutes after the start of the experiment, the volume of the gas was 10 m310\text{ m}^310 m3.

Find the value of TTT according to the model, giving your answer to one decimal place.

[3]

1.10.8 Numerical methods to solve problems (A-level only) Questions

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