1.8.7 Reduce y = ax^n and y = ab^x to linear form

Easy Medium

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Question 24

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

C = pq^d

where $p$ and $q$ are positive constants.

A graph shows a linear relationship between $log_{10} C$ and $d$ . The line passes through the points $(0, 0.85)$ and $(12, 1.45)$ .

Find, to 3 decimal places, the value of $p$ and the value of $q$ .

[4]

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]