The graph below shows the trend in the number of cases of people infected with the coronavirus in a particular country. Jamie claims that the trend shown is approximated by a linear equation of the form y=320xy = 320x, where xx is the number of days and yy is the number of infections. Explain why she is wrong.

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Worked solution

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1. Identify why the graph does not support the stated linear model

The vertical axis is not a normal linear scale, since 10,100,1000,1000010,100,1000,10000 are equally spaced. It is a logarithmic scale. Therefore, the dashed straight line on the graph is not evidence that yy is directly proportional to xx, so the trend cannot be approximated by y=320xy=320x from this graph.

Answer

Jamie is wrong because the vertical axis is on a logarithmic scale: the labels 10,100,1000,1000010,100,1000,10000 are equally spaced. Hence a straight line on this graph does not represent a linear relationship y=320xy=320x in the actual number of infections.

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