Question

franc earns $15 an hour as a delivery driver his company also pays him $30 a week for car maintenance. What function that describes franc's weekly earnings? what is the rate of change for this situation be sure to iclude the units.

Answer 1

Explanation:

Franc's Weekly Earnings Function and Rate of Change

Function:



Franc's weekly earnings can be described by a linear function where:



h: represents the number of hours worked in a week.

E(h): represents Franc's weekly earnings in dollars.

Since Franc earns a fixed $30 for car maintenance and $15 per hour worked, the function is:



E(h) = 15h + 30



This function represents a direct proportion between the number of hours worked (h) and Franc's earnings (E(h)). As the number of hours worked increases, so does Franc's earnings, at a constant rate of $15 per hour.



Rate of Change:



The rate of change for this situation is represented by the slope of the linear function. In this case, the slope is 15 dollars per hour. This means that for every additional hour Franc works, his earnings increase by $15.



Units:



The independent variable (h) is measured in hours.

The dependent variable (E(h)) is measured in dollars.

The rate of change is measured in dollars per hour.

Visualization:



Imagine a graph where the x-axis represents the number of hours worked and the y-axis represents Franc's weekly earnings. The graph would be a straight line with a slope of 15. This line would intercept the y-axis at $30 (Franc's car maintenance allowance), regardless of the number of hours worked.

Answer 2

`\sf Function: E(h) = 15h + 30`

Rate of change: 15 dollars per hour (or $15/hour)

Explanation:

Let E represent Franc's weekly earnings in dollars, and h represent the number of hours he works in a week. The function that describes Franc's weekly earnings (E) can be expressed as:

`\sf E(h) = 15h + 30`

Here:

• 15h represents the amount he earns per hour.
• 30 is the fixed amount he receives weekly for car maintenance.

The rate of change, often referred to as the derivative in calculus, represents how much the dependent variable changes concerning the independent variable.

In this context, the rate of change of Franc's weekly earnings with respect to the number of hours worked is the coefficient of h, which is 15.

Therefore, the rate of change for this situation is 15 dollars per hour (or $15/hour).