1.8 Exponentials and Logarithms

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Question 44

A conservationist monitors the population of a rare lizard species on a remote island. The population, $P$ , was recorded every 5 years from 1 January 2000 until 2025. The population size is modelled by the equation

P = km^n

where $n$ is the number of years since 1 January 2000 and $k$ and $m$ are constants.

Show that $P = km^n$ can be written as $log_{10} P = \log_{10} k + n \log_{10} m$ .

[2]

The values of $log_{10} P$ against $n$ are plotted on a graph, and a line of best fit is drawn. The line of best fit passes through the points $(0, 1.48)$ and $(25, 2.73)$ . Find estimates for the values of $k$ and $m$ , giving your answers to three significant figures.

[4]

Use your model to predict the year in which the lizard population will first reach 2000.

[2]

Comment on the reliability of your prediction in part (c).

[1]

1.8 Exponentials and Logarithms

Question 44

P = km^n

where $n$ is the number of years since 1 January 2000 and $k$ and $m$ are constants.

Show that $P = km^n$ can be written as $log_{10} P = \log_{10} k + n \log_{10} m$ .

[2]

[4]

Use your model to predict the year in which the lizard population will first reach 2000.

[2]

Comment on the reliability of your prediction in part (c).

[1]

1.8 Exponentials and Logarithms

Question 44

Markscheme

1.8 Exponentials and Logarithms

Question 44

Markscheme

1.8 Exponentials and Logarithms

Question 44

1.8 Exponentials and Logarithms Questions

1.8 Exponentials and Logarithms

Question 44

1.8 Exponentials and Logarithms Questions