Skip to content

Course home

3.8 Numerical Methods (A-level only)

3.8 Numerical Methods (A-level only)

EasyMediumHard
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109
Question 62

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]
Markscheme

3.8 Numerical Methods (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3.8 Numerical Methods (A-level only)

129 exam-style questions on WJEC A Level Maths 3.8 Numerical Methods (A-level only), covering 3.8.1 Numerical Methods (A-level only), 3.8.2 Numerical Methods (A-level only), 3.8.3 Numerical Methods (A-level only), 3.8.4 Numerical Methods (A-level only), and 3.8.5 Numerical Methods (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

Question bank