The W-4 is the "formula" for estimating your taxes. The problem is that the tax "value" of a dependent changes based on their age, so to really be accurate, you should update your W-4 whenever you have life events that may change your taxes. A child turning 17, so the credit is reduced in value, is one such event. If your child goes to college and you can claim an education credit, that is a life event that reduces your tax so you could have less withholding. Gifts to charity, buying a home, etc., are all life events that might change your taxes and so you have the ability to account for them in your withholding.
The only other way to do it would be to prepare a mock tax return on January 1 of the year, estimate your tax obligation, divide by 52 weeks or 12 months or however you are paid, and give that amount manually to your employer to be withheld. And in reality, that's what the W-4 does (more or less), just with the majority of the calculations hidden from you and performed by the IRS or the employer's payroll software.
