## 1.7 Linearisation Using Exponentials

Note: if you cannot remember the appearance of graphs of the form y=kx^{n}, revise notes for 1.6 Exponential Graphs.

### Linearisation using x^{-1}

- If a
**scatterplot**appears to show a relationship of the form y=kx^{-1}, it can be linearised by taking the**inverse**of the data points.

Example

X |
Y |

1 |
1 |

2 |
0.5 |

3 |
0.29 |

4 |
0.25 |

5 |
0.21 |

6 |
0.17 |

7 |
0.14 |

A company running a streaming service records the proportion of first-time users which return to the service over a period of 7 months, the results are plotted above. They require the data to be linearised in order to perform further analysis. From the dot plot, we can see that the relationship appears to be of the form: y=kx^{-1} and so we will take the inverse of the x data in order to linearise it:

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