Tenant gave 30 day notice....help.

[Daniel Luedtke]

So, a tenant in my triplex just gave their 30 day notice this morning. They have been on a month to month lease the last couple months, and I just gave them a new lease to sign last week. She informed they will not be signing the new lease, and gave notice. She said she just got a call and accepted to a new apt and will be moving Oct 6. Do I still have a right to collect the full 30 days of rent thru their 30 days from notice? Obviously I could pro-rate the rent if I found a new tenant sooner. Can I collect Oct. rent (prorated) thru their 30 days still? Thoughts and advice much appreciated!