Question

the table below represents the number of miles, y, that the satellite space explorer flies in x hours. find the rate of change.

space explorer

hours (x)	miles (y)
13	59800
17	78200
21	96600

Explanation:

Step1: Recall rate of change formula

The rate of change (slope) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \(\frac{y_2 - y_1}{x_2 - x_1}\).

Step2: Choose two points from the table

Let's take the first two points: \((x_1, y_1)=(9, 41400)\) and \((x_2, y_2)=(13, 59800)\).

Step3: Calculate the rate of change

Substitute into the formula: \(\frac{59800 - 41400}{13 - 9}=\frac{18400}{4}=4600\).
We can check with another pair, e.g., \((13, 59800)\) and \((17, 78200)\): \(\frac{78200 - 59800}{17 - 13}=\frac{18400}{4}=4600\). Another pair \((17, 78200)\) and \((21, 96600)\): \(\frac{96600 - 78200}{21 - 17}=\frac{18400}{4}=4600\). So the rate of change is consistent.

Answer:

4600