Question

A math tutor makes $15.00 per hour in the tutoring lab at her school. She earns an additional $7.50 more per hour overtime for any hours worked which exceed her normal 40-hr work week. Write a piece-wise function to describe the tutors weekly pay P(h), in terms of hours, h. ​

Answer 1

To describe the tutor's weekly pay P(h) in terms of hours, h, we can write a piece-wise function. If h is less than or equal to 40, the tutor's pay is $15.00 per hour. If h is greater than 40, the tutor's pay is $15.00 per hour for the first 40 hours and an additional $7.50 per hour for any hours beyond 40.

Step-by-step explanation:

To write a piece-wise function to describe the tutor's weekly pay P(h), we need to consider two cases: h is less than or equal to 40 and h is greater than 40.

For the first case, when h is less than or equal to 40, the tutor's weekly pay is P(h) = 15h. This is because the tutor earns $15.00 per hour for the normal 40-hour work week.

For the second case, when h is greater than 40, the tutor's weekly pay is P(h) = 15(40) + 7.50(h - 40). This is because the tutor earns $15.00 per hour for the normal 40-hour work week and an additional $7.50 per hour for any hours worked beyond 40.

Answer 2

P(h) = 15h if 0 ≤ h ≤ 40, 7.5h + 300 if h > 40