An environmental scientist, Dr. Aris, believes the population of a certain species of fish in a lake, recorded as P P\,P thousands, has been growing exponentially since 2012. Dr. Aris models the population using the formula
P=a×bt P = a \times b^{t} P=a×btwhere t t\,t is the number of years since 2012 and a a\,a and b b\,b are constants.
He plots a graph of log10P\log_{10} Plog10P against t t\,t and determines the equation of the line of best fit to be:
log10P=0.041t+1.32 \log_{10} P = 0.041t + 1.32 log10P=0.041t+1.32(i) Show that, correct to three significant figures, a=20.9a = 20.9a=20.9.
(ii) Find the value of bbb, giving your answer to three significant figures.
According to the model, state the yearly percentage increase in the fish population.
(i) Use the model to predict the fish population in the year 2028.
(ii) Explain why the prediction made in part (c)(i) may be unreliable.
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.
