Question

James works for a delivery company. He gets paid a flat rate of $5 each day he works, plus an additional amount of money for every delivery he makes. The total amount of money he earns per day is a function of the number of deliveries he makes, as represented on the graph below. Part A: Enter the rate of change for the money earned, measured as dollars per delivery, between 0 and 2 deliveries. $ ___ fill in the box with the answer Part B: Which of the following statements correctly compares the rate of change for the money earned, measured as dollars per delivery, between 2 and 4 deliveries and 6 and 8 deliveries? The rate of change is the same between the two time intervals. The rate of change is larger between 2 and 4 deliveries than 6 to 8 deliveries. The rate of change is smaller between 2 and 4 deliveries than 6 to 8 deliveries. The rate of change is a positive value between 2 and 4 deliveries and a negative value between 6 and 8 deliveries.

Answer 1

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.

Explanation:

The rate of change for a variables based on another variable is known as the slope.

The formula to compute the slope is:

(a)

Compute the rate of change for the money earned, measured as dollars per delivery, between 0 and 2 deliveries as follows:

For, x₁ = 0 and x₂ = 2 deliveries the money earned are y₁ = $5 and y₂ = $9.

The rate of change for the money earned is:

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, x₁ = 2 and x₂ = 4 deliveries the money earned are y₁ = $9 and y₂ = $13.

The rate of change for the money earned is:

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, x₁ = 6 and x₂ = 8 deliveries the money earned are y₁ = $17 and y₂ = $21.

The rate of change for the money earned is:

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.

Answer 2

(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.

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}=(y_(2)-y_(1))/(x_(2)-x_(1))`

(a)

Compute the rate of change for the money earned, measured as dollars per delivery, between 0 and 2 deliveries as follows:

For, x₁ = 0 and x₂ = 2 deliveries the money earned are y₁ = $5 and y₂ = $9.

The rate of change for the money earned is:

`\text{Slope}=(y_(2)-y_(1))/(x_(2)-x_(1))`

`=(9-5)/(2-0)\\\\=(4)/(2)\\\\=2`

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, x₁ = 2 and x₂ = 4 deliveries the money earned are y₁ = $9 and y₂ = $13.

The rate of change for the money earned is:

`\text{Slope}=(y_(2)-y_(1))/(x_(2)-x_(1))`

`=(13-9)/(4-2)\\\\=(4)/(2)\\\\=2`

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, x₁ = 6 and x₂ = 8 deliveries the money earned are y₁ = $17 and y₂ = $21.

The rate of change for the money earned is:

`\text{Slope}=(y_(2)-y_(1))/(x_(2)-x_(1))`

`=(17-21)/(8-6)\\\\=(4)/(2)\\\\=2`

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.