Whether the technology company could enforce the provision depends on a number of factors, all of which are weighed and balanced against each other. These include:
* The time frame of the non-compete (yours, you say, is three years)
* Whether there's any geographic scope to the non-compete (are you prevented from working in Michigan, or anywhere in the U.S.?)
* Whether there are any industry limitations (e.g., prevented from working for any kind of company or only financial services companies)
* The level of expertise you have/access to confidential information you obtained (in other words, were you an essential, high-level executive, or just part of the IT pool?).
The last thing you need, though, is to be hauled into court to fight this out. Bring your non-compete agreement to an employment attorney in your state to evaluate the risks of moving forward in light of its wording.