An ecological study tracked the expansion of an invasive water lily population in a lake starting on 1 March. The total surface area covered by the lilies, S S\,S square metres, was recorded over several months. The area is modelled by the equation
S=abt S = ab^t S=abtwhere t t\,t is the number of months since 1 March, and a a\,a and b b\,b are constants.
Show that S=abtS = ab^tS=abt can be written in the form log10S=log10a+tlog10b\log_{10} S = \log_{10} a + t \log_{10} blog10S=log10a+tlog10b.
The values of log10S\log_{10} Slog10S against t t\,t are plotted on a graph using data collected for 0≤t≤80 \leq t \leq 80≤t≤8, and a line of best fit is drawn. The line passes through the points (0,1.48)(0, 1.48)(0,1.48) and (8,3.72)(8, 3.72)(8,3.72). Find estimates for the values of a a\,a and bbb. Give your answers to three significant figures.
Use the model to predict the month in which the surface area covered by the lilies will first exceed 25,000 m2m^2m2.
State one reason why the prediction in part (c) may be unreliable.
278 exam-style questions on CCEA A Level Maths 2.5 Data presentation and interpretation, covering 2.5.1 Data presentation and interpretation, 2.5.2 Data presentation and interpretation, 2.5.3 Data presentation and interpretation, 2.5.4 Data presentation and interpretation, 2.5.5 Data presentation and interpretation, 2.5.6 Data presentation and interpretation, 2.5.7 Data presentation and interpretation, 2.5.8 Data presentation and interpretation, 2.5.9 Data presentation and interpretation, and 2.5 Data presentation and interpretation. Each one has a worked solution and a mark scheme showing where the marks go.