Lease agreement with option to change move in date

[Chatree C.]

There's a good prospective tenant that wants to sign our lease but they are not sure about start date (work travel schedule) until 3 weeks from now. And they agree if they start later, they are willing to pay a bit more to make up for loss rent.

For example:

rent is $2000 if starting Aug 1

rent is $2100 if starting Aug 8

rent is $2200 if starting Aug 15

We need the contract signed before they can make this decision, can we pick a date to sign first then include a clause where they have until X date to change the start date & rent?