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1 Unit AS 1: Pure Mathematics

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Question 403

A marine biologist is investigating the metabolic activity of a specific phytoplankton colony in a controlled bioreactor. The rate of oxygen evolution, RRR, measured in micromoles per second (μmol s−1\mu\text{mol s}^{-1}μmol s−1), is modelled by the function

R=54I−4I32−120,I>0 R = 54I - 4I^{\frac{3}{2}} - 120, \quad I > 0 R=54I−4I23​−120,I>0

where III is the light intensity delivered to the colony in kilolux.

According to this model:

a.

find, using calculus, the maximum possible rate of oxygen evolution.

[4]
b.

Justify, also using calculus, that the rate you have found is a maximum.

[3]
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1 Unit AS 1: Pure Mathematics Questions

  1. A Level
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  3. /1 Unit AS 1: Pure Mathematics

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