Question

4. The following table contains the population of Ontario from 2011 pacing to 2019.

a. Determine whether the following relation is linear or non-linear using first differences.

Answer 1

To calculate the first differences, you can subtract the population value of the previous year from the population value of the current year. For example, the first difference for the year 2012 would be calculated as 13.01 million (the population in 2012) minus 12.85 million (the population in 2011), which equals 0.16 million.

Here are the first differences for each year:

| Year | Population (Millions of people) | First difference |

|------|---------------------------------|------------------|

| 2011 | 12.85 | |

| 2012 | 13.01 | 0.16 |

| 2013 | 13.18 | 0.17 |

| 2014 | 13.36 | 0.18 |

| 2015 | 13.55 | 0.19 |

| 2016 | 13.75 | 0.20 |

| 2017 | 13.96 | 0.21 |

| 2018 | 14.19 | 0.23 |

| 2019 | 14.57 | 0.38 |

As you can see, the first differences are not constant, which means that the relation between the year and population is non-linear.