Question 19 – 1.8.7 Reduce y = ax^n and y = ab^x to linear form - Questions

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, $S\,$ square metres, was recorded over several months. The area is modelled by the equation

S = ab^t

where $t\,$ is the number of months since 1 March, and $a\,$ and $b\,$ are constants.

Show that $S = ab^t$ can be written in the form $log_{10} S = \log_{10} a + t \log_{10} b$ .

The values of $log_{10} S$ against $t\,$ are plotted on a graph, and a line of best fit is drawn. The line passes through the points $(0, 1.48)$ and $(8, 3.72)$ . Find estimates for the values of $a\,$ and $b$ . 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 $m^2$ .

State one reason why the prediction in part (c) may be unreliable.

S = ab^t

where $t\,$ is the number of months since 1 March, and $a\,$ and $b\,$ are constants.

Show that $S = ab^t$ can be written in the form $log_{10} S = \log_{10} a + t \log_{10} b$ .

Use the model to predict the month in which the surface area covered by the lilies will first exceed 25,000 $m^2$ .

State one reason why the prediction in part (c) may be unreliable.

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

Question 18

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

Question 18

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

Question 18

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

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

Question 18

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