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We want to know if the function given in the following table has a constant rate of change.

Time (s), $x$ | Distance (m), $y$ |
---|---|

$4.82$ | $40$ |

$6.49$ | $60$ |

$8.13$ | $80$ |

$9.69$ | $100$ |

We can check the rate of change algebraically by noting the change in $x$ and change in $y$ between each of the data points.

We find the rate of change between each row by dividing the change in $y$ by the change in $x.$ $rate of change=change inxchange iny $ Let's find the rate of change between the first two rows.$rate of change=change inxchange iny $

$rate of change=1.6720 $

UseCalcUse a calculator

$rate of change=11.97604…$

RoundDecRound to ${\textstyle 2 \, \ifnumequal{2}{1}{\text{decimal}}{\text{decimals}}}$

$rate of change≈11.98$

Changes between rows | $change inxchange iny $ | Rate of change |
---|---|---|

$1_{st}→2_{nd}$ | $1.6720 $ | $≈11.98$ |

$2_{nd}→3_{rd}$ | $1.6420 $ | $≈12.20$ |

$3_{rd}→4_{th}$ | $1.5620 $ | $≈12.82$ |

As we can see, the rate of change is not constant. The runner had a higher average speed later in the race than in the middle.

b

We have been asked to find if the function given by the following table has a constant rate of change.

Time (s), $x$ | Floor number, $y$ |
---|---|

$0$ | $18$ |

$1.6$ | $20$ |

$3.2$ | $22$ |

$4.8$ | $24$ |

Let's find the change in $x$ and change in $y$ between each of the rows.

We can find the rate of change between each set of points by using the following relationship. $rate of change=change inxchange iny $ We will now find the rate of change for the first two points.$rate of change=change inxchange iny $

$rate of change=1.62 $

UseCalcUse a calculator

$rate of change=1.25$

Changes between rows | $change inxchange iny $ | Rate of change |
---|---|---|

$1_{st}→2_{nd}$ | $1.62 $ | $1.25$ |

$2_{nd}→3_{rd}$ | $1.62 $ | $1.25$ |

$3_{rd}→4_{th}$ | $1.62 $ | $1.25$ |

As we can see, the rate of change is constant. It tells us that the elevator's speed is $1.25$ floors/second.