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1.9.15 Rates of change with the chain rule (A-level only)

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Question 22

The concentration, CCC mg/L, of a chemical catalyst in a bio-reactor, ttt hours after the reaction begins, is modeled by the equation

C=L+240e−rt C = L + 240e^{-rt} C=L+240e−rt

where LLL and rrr are positive constants. Given that the initial concentration of the catalyst is 275275275 mg/L,

a.

find the value of LLL.

[1]
b.

The concentration of the catalyst 5 hours after the reaction begins is 110110110 mg/L.

Show that r=pln⁡qr = p \ln qr=plnq where ppp and qqq are rational numbers to be found.

[3]
c.

Hence find

the concentration of the catalyst 10 hours after the reaction begins, giving your answer to 3 significant figures,

[2]
d.

the rate of decrease of the concentration of the catalyst 10 hours after the reaction begins. Give your answer in mg/L h−1\text{mg/L h}^{-1}mg/L h−1 to 3 significant figures.

[3]

1.9.15 Rates of change with the chain rule (A-level only) Questions

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