11.

Wendy is paid $12 per hour and plans to work between 30 and 35 hours per week. Identify the independent and dependent quantity in the situation. Find reasonable domain and range values.

1 answer

In this situation, we can identify the following:

Independent Quantity: The number of hours Wendy works, which can vary between 30 and 35 hours per week. This is the quantity that Wendy can choose or control.

Dependent Quantity: Wendy's weekly pay, which depends on the number of hours she works. The more hours she works, the more she earns.

Reasonable Domain and Range Values:

  • Domain (independent quantity): The number of hours Wendy plans to work ranges from 30 to 35 hours per week. Thus, the reasonable domain is given by: \[ 30 \leq h \leq 35 \] where \( h \) represents the number of hours worked.

  • Range (dependent quantity): Wendy's pay can be calculated using the formula: \[ \text{Pay} = \text{Hourly Rate} \times \text{Hours Worked} = 12h \] Substituting the values from the domain:

    • If she works 30 hours: \[ \text{Pay} = 12 \times 30 = 360 \]
    • If she works 35 hours: \[ \text{Pay} = 12 \times 35 = 420 \]

Thus, the reasonable range for Wendy's weekly pay is: \[ 360 \leq P \leq 420 \] where \( P \) represents Wendy's weekly pay.

In summary:

  • Independent Quantity: Hours worked (30 to 35 hours)
  • Dependent Quantity: Weekly pay ($360 to $420)
  • Domain: \( [30, 35] \)
  • Range: \( [360, 420] \)