Question

4. A math tutor makes $12 an hour for the first 40 hours she works during a week and $24 an hour for each hour over 40 hours. As an exercise for her students, she had them graph her total weekly pay in dollars as it relates to her number of hours worked. Now you will do the same. (6 points: Part I - 1 point; Part II - 2 points; Part III - 1 point; Part IV - 2 points)

Part I: What equation models the tutor's total weekly pay y in dollars as it relates to the number of hours x that she has worked if the tutor has worked 40 hours or fewer?








Part II: What equation models the tutor's total weekly pay y in dollars as it relates to the number of hours x that she has worked if the tutor has worked more than 40 hours?








Part III: Combine the slope-intercept equations found in parts I and II into one piecewise equation.








Part IV: Graph the tutor's total weekly pay in dollars as it relates to her number of hours worked by using the piecewise equation from part III and the coordinate grid below.

Answer 1

See below

Explanation:

Part I

When x ≤ 40, the equation is

• y = 12x

Part II

When x > 40

• y = 12*40 + 24(x - 40) ⇒
• y = 24x - 960 + 480 ⇒
• y = 24x - 480

Part III

`y = \left \{ {12x, if x < or = 40 \atop {24x - 480, if x>40}} \right. \\`

Part IV

The graph is attached