1.12 I: Numerical methods (A-level only)

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Question 64

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

\frac{150 \lambda e^{0.15t}}{\lambda e^{0.15t} + 12}

where $λ\lambda$ is a positive constant.

Given that:

The initial concentration of the catalyst at the start of the process was $30$ mg/L.
The concentration reached $90$ mg/L after $T$ minutes.

Show that $λ=3\lambda = 3$ .

[4]

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

[3]

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

[2]

1.12 I: Numerical methods (A-level only)

Question 64

\frac{150 \lambda e^{0.15t}}{\lambda e^{0.15t} + 12}

where $λ\lambda$ is a positive constant.

Given that:

The initial concentration of the catalyst at the start of the process was $30$ mg/L.
The concentration reached $90$ mg/L after $T$ minutes.

Show that $λ=3\lambda = 3$ .

[4]

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

[3]

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

[2]

1.12 I: Numerical methods (A-level only)

Question 64

1.12 I: Numerical methods (A-level only) Questions

1.12 I: Numerical methods (A-level only)

Question 64

1.12 I: Numerical methods (A-level only) Questions