Question

1. a nurse earns $450 per week for working 40 hours plus $15 per hour worked over 40 hours. a nurse can work a maximum of 60 hours per week. which graph best represents the nurses weekly earnings in dollars for working h hours over 40?

Explanation:

Step1: Define the earnings function

Let $h$ be the number of hours worked over 40. The base - pay is $450$ for the first 40 hours. The additional pay for $h$ hours over 40 is $15h$. So the total weekly earnings $E$ is given by the function $E = 450+15h$.

Step2: Determine the domain of $h$

The nurse can work a maximum of 60 hours per week. Since the base - pay is for 40 hours, the number of hours $h$ over 40 satisfies $0\leq h\leq20$.

Step3: Analyze the properties of the function

The function $E = 450 + 15h$ is a linear function with a slope of 15 and a $y$ - intercept of 450 (when $h = 0$, $E=450$). As $h$ increases from 0 to 20, $E$ will increase. When $h = 0$, $E = 450$, and when $h = 20$, $E=450+15\times20=450 + 300=750$.

The graph will be a line segment starting at the point $(0,450)$ and ending at the point $(20,750)$ with a positive slope of 15.

Answer:

The graph is a line segment with a slope of 15, starting at the point $(0,450)$ and ending at the point $(20,750)$ (where the $x$ - axis represents the number of hours $h$ over 40 and the $y$ - axis represents the weekly earnings in dollars).