Generally, working nine consecutive days does not by itself entitle an employee to overtime in Michigan.
For most nonexempt employees, Michigan requires overtime at 1½ times the regular rate for hours worked over 40 in a 7-day workweek. Federal law follows the same basic rule.
The important point is that a “workweek” is a fixed period of 7 consecutive 24-hour days established by the employer. It does not necessarily correspond to Monday through Sunday, and each workweek is normally considered separately.
Therefore, it is possible to legally work nine consecutive days without earning overtime. For example, if those nine days are divided between two established workweeks and you work only 32 hours in one week and 40 hours in the next, the consecutive-day count itself does not trigger overtime.
However, an employer cannot simply move the workweek around from week to week to avoid paying overtime. Once the workweek is established, it generally remains fixed; a change must be intended as a genuine permanent change rather than a device to evade overtime requirements.
So the first thing I would ask your employer is: “What is the company's established 7-day workweek for overtime purposes?” Then add up your actual hours within each of those workweeks. If you exceeded 40 hours in either one and are a nonexempt employee, you generally should receive overtime for the excess hours.