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1.6 Exponentials and logarithms

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Question 53

An environmental engineer is monitoring the concentration of a specific organic compound, CCC mg/L, in a testing chamber. The concentration ddd days after the start of the observation is modelled by the equation

C=pqd C = pq^d C=pqd

where ppp and qqq are positive constants.

A graph shows a linear relationship between log⁡10C\log_{10} Clog10​C and ddd. The line passes through the points (0,0.85)(0, 0.85)(0,0.85) and (12,1.45)(12, 1.45)(12,1.45).

a.

Find, to 3 decimal places, the value of ppp and the value of qqq.

[4]
b.

Using the model with the values found in part (a), find the rate of increase of the concentration of the compound, in mg/L per day, exactly 8 days after the start of the study. Give your answer to 2 decimal places.

[3]

1.6 Exponentials and logarithms Questions

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