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=pqdwhere ppp and qqq are positive constants.
A graph shows a linear relationship between log10C\log_{10} Clog10C 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).
Find, to 3 decimal places, the value of ppp and the value of qqq.
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.
Practise Edexcel A Level Maths Regression, Correlation and Hypothesis Testing with exam-style questions for A Level Maths. 202 questions covering Exponential Models, Measuring Correlation, and Hypothesis Testing for Zero Correlation, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
