Question

Jan works from 30 to 40 hours per week during the summer. she earns $12.00 per hour. her friend rachel also has a job. rachel's pay for t hours is given by the function r(t) = 11t, where 20 ≤ t ≤ 30. find the domain and range of each function. compare their hourly wages and the amount they earn per week.

Answer 1

Jan's function has a domain of [30, 40] and a range of [$360, $480]. Rachel's function has a domain of [20, 30] and a range of [$220, $330]. Jan earns $12 per hour and can earn between $360 and $480 per week, while Rachel earns $11 per hour and can earn between $220 and $330 per week.

Step-by-step explanation:

The domain of Jan's function is the range of hours she works per week, which is between 30 and 40, denoted by [30, 40]. The range of Jan's function is the amount of money she earns per week, which is calculated by multiplying her hourly wage ($12) by the number of hours she works (30 to 40 hours). So, the range of Jan's function is [$360, $480].

Similarly, Rachel's function is given by r(t) = 11t, where t represents the number of hours she works per week. The domain of Rachel's function is the range of hours she works per week, which is between 20 and 30, denoted by [20, 30]. The range of Rachel's function is the amount of money she earns per week, calculated by multiplying her hourly wage ($11) by the number of hours she works (20 to 30 hours). So, the range of Rachel's function is [$220, $330].

Comparing their hourly wages, Jan earns $12 per hour while Rachel earns $11 per hour. Comparing the amount they earn per week, Jan can earn between $360 and $480 per week while Rachel can earn between $220 and $330 per week.

Answer 2

Jan earns between $360 and $480. While Rachel earns between $220 and $330. Jan's hourly wage is $12 and Rachel's is $11.