Question

Gillian works from 20 to 30 hours per week during the summer. She earns $12.50 per hour. Her friend Emily also has a job. Her pay for hours each week is given by the function e(t) = 13t, where 15 ≤ t < 25.

a. Find the domain and range of each function.
b. Compare their hourly wages and the amount they earn per week.

Answer 1

Gillian has a lower hourly wage but can potentially earn more per week due to more available working hours. Emily earns a higher hourly wage but has a smaller range of working hours, resulting in slightly lower maximum weekly earnings.

Step-by-step explanation:

The student's question involves analyzing the wage and earnings of two individuals, Gillian and Emily, and how they relate to hours of work with given pay rates and functions for their earnings.

Gillian's Wages

Domain: The possible number of hours Gillian can work, which is from 20 to 30 hours.

Range: The possible earnings, which would be from $250 (20 hours × $12.50) to $375 (30 hours × $12.50).

Emily's Wages

Domain: The number of hours Emily can work as defined by the function e(t), which is from 15 to just under 25 hours.

Range: Calculated by substituting the domain values into the function e(t) = 13t, which gives a range from $195 (15 hours × $13) to $325 (just under 25 hours × $13).

Comparison

Gillian earns less per hour than Emily, at $12.50 compared to Emily's $13. However, Gillian has the potential to earn more per week since her range of hours is 20 to 30, compared to Emily's 15 to just under 25. Gillian's maximum weekly earnings are $375, while Emily's maximum, without hitting 25 hours, is slightly less.