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1.6.17 Sequences and series in modelling (A-level only)

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Question 21

In this question you must show detailed reasoning.

A manufacturing plant is implementing a 12-month program to reduce its industrial effluent. The effluent discharge is monitored at the start of each month.

  • In month 1, the effluent discharge is 150 m³.
  • In month 12, the effluent discharge is 51 m³.

The plant managers are evaluating two different reduction strategies.

Under strategy Plan A, the volume of effluent discharged will decrease by the same constant amount each month.

a.

Calculate the effluent discharge in month 7 under Plan A. (3)

[3]
b.

Under strategy Plan B, the volume of effluent discharged will decrease by a constant percentage each month.

Calculate the effluent discharge in month 7 under Plan B. Give your answer in m³ to one decimal place. (3)

[3]
c.

The plant also generates a fixed volume of runoff, yyy m³, each month over the 12-month period. Given that:

  • yyy is an integer
  • the total volume of effluent and runoff produced over the 12 months must not exceed 1500 m³.

(i) Find the maximum value of yyy, if strategy Plan A is used. (ii) Find the maximum value of yyy, if strategy Plan B is used. (5)

[5]

1.6.17 Sequences and series in modelling (A-level only) Questions

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