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1.9.7 Numerical methods in context (A-level only)

Medium
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Question 3

An industrial chemist is monitoring the concentration of a catalyst, CCC mg/L, in a pressurized chemical reactor. The concentration at time ttt minutes after the reaction begins is modelled by the equation

C=150λe0.15tλe0.15t+12 C = \frac{150 \lambda e^{0.15t}}{\lambda e^{0.15t} + 12} C=λe0.15t+12150λe0.15t​

where λ\lambdaλ is a positive constant.

Given that:

  • The initial concentration of the catalyst at the start of the process was 303030 mg/L.
  • The concentration reached 909090 mg/L after TTT minutes.
a.

Show that λ=3\lambda = 3λ=3.

[4]
b.

Calculate the value of TTT, giving your answer to one decimal place. (Solutions relying entirely on graphical or numerical methods are not acceptable.)

[3]
c.

Determine, according to this model, the maximum possible concentration of the catalyst as time increases.

[2]

1.9.7 Numerical methods in context (A-level only) Questions

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