Answer:
(a) The rate of change for the money earned, measured as dollars per delivery, between 0 and 2 deliveries is $2.
(b) The rate of change is the same between the two time intervals.
Step-by-step explanation:
The rate of change for a variables based on another variable is known as the slope.
The formula to compute the slope is:
![\text{Slope}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}](https://tex.z-dn.net/?f=%5Ctext%7BSlope%7D%3D%5Cfrac%7By_%7B2%7D-y_%7B1%7D%7D%7Bx_%7B2%7D-x_%7B1%7D%7D)
(a)
Compute the rate of change for the money earned, measured as dollars per delivery, between 0 and 2 deliveries as follows:
For, <em>x</em>₁ = 0 and <em>x</em>₂ = 2 deliveries the money earned are <em>y</em>₁ = $5 and <em>y</em>₂ = $9.
The rate of change for the money earned is:
![\text{Slope}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}](https://tex.z-dn.net/?f=%5Ctext%7BSlope%7D%3D%5Cfrac%7By_%7B2%7D-y_%7B1%7D%7D%7Bx_%7B2%7D-x_%7B1%7D%7D)
![=\frac{9-5}{2-0}\\\\=\frac{4}{2}\\\\=2](https://tex.z-dn.net/?f=%3D%5Cfrac%7B9-5%7D%7B2-0%7D%5C%5C%5C%5C%3D%5Cfrac%7B4%7D%7B2%7D%5C%5C%5C%5C%3D2)
Thus, the rate of change for the money earned, measured as dollars per delivery, between 0 and 2 deliveries is $2.
(b)
Compute the rate of change for the money earned, measured as dollars per delivery, between 2 and 4 deliveries as follows:
For, <em>x</em>₁ = 2 and <em>x</em>₂ = 4 deliveries the money earned are <em>y</em>₁ = $9 and <em>y</em>₂ = $13.
The rate of change for the money earned is:
![\text{Slope}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}](https://tex.z-dn.net/?f=%5Ctext%7BSlope%7D%3D%5Cfrac%7By_%7B2%7D-y_%7B1%7D%7D%7Bx_%7B2%7D-x_%7B1%7D%7D)
![=\frac{13-9}{4-2}\\\\=\frac{4}{2}\\\\=2](https://tex.z-dn.net/?f=%3D%5Cfrac%7B13-9%7D%7B4-2%7D%5C%5C%5C%5C%3D%5Cfrac%7B4%7D%7B2%7D%5C%5C%5C%5C%3D2)
The rate of change for the money earned, measured as dollars per delivery, between 2 and 4 deliveries is $2.
Compute the rate of change for the money earned, measured as dollars per delivery, between 6 and 8 deliveries as follows:
For, <em>x</em>₁ = 6 and <em>x</em>₂ = 8 deliveries the money earned are <em>y</em>₁ = $17 and <em>y</em>₂ = $21.
The rate of change for the money earned is:
![\text{Slope}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}](https://tex.z-dn.net/?f=%5Ctext%7BSlope%7D%3D%5Cfrac%7By_%7B2%7D-y_%7B1%7D%7D%7Bx_%7B2%7D-x_%7B1%7D%7D)
![=\frac{17-21}{8-6}\\\\=\frac{4}{2}\\\\=2](https://tex.z-dn.net/?f=%3D%5Cfrac%7B17-21%7D%7B8-6%7D%5C%5C%5C%5C%3D%5Cfrac%7B4%7D%7B2%7D%5C%5C%5C%5C%3D2)
The rate of change for the money earned, measured as dollars per delivery, between 6 and 8 deliveries is $2.
Thus, the rate of change is the same between the two time intervals.