Question 65 – 3.7 Numerical methods (A-level only) - Questions

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 $λ=3\lambda = 3$ .

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

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

\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 $λ=3\lambda = 3$ .

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

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

3.7 Numerical methods (A-level only)

Question 64

3.7 Numerical methods (A-level only)

Question 64

3.7 Numerical methods (A-level only)

Question 64

3.7 Numerical methods (A-level only) Questions

3.7 Numerical methods (A-level only)

Question 64

3.7 Numerical methods (A-level only) Questions