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1.11.8 Interpreting solutions of differential equations (A-level only)

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Question 8

In a controlled chemical synthesis, the rate of production of a particular polymer, R kg h−1R\text{ kg h}^{-1}R kg h−1, is modelled by the equation:

R=20.4−20.0e−0.5t−0.4e0.25t R = 20.4 - 20.0e^{-0.5t} - 0.4e^{0.25t} R=20.4−20.0e−0.5t−0.4e0.25t

where ttt is the time in hours since the reaction vessel was activated.

a.

Determine the maximum production rate predicted by the model, giving your answer to one decimal place. Fully justify your answer.

[5]
b.

Derive an expression for the total mass of polymer produced, M kgM\text{ kg}M kg, in terms of ttt.

[4]
c.

After 15 hours, the total mass of polymer produced was measured to be 200 kg. Comment on the accuracy of the model.

[1]

1.11.8 Interpreting solutions of differential equations (A-level only) Questions

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