The following script provides an educated guess regarding database growth

It does this by examining the size of backups. It queries MSDB for backup sizes, calculated the difference, divided by the number of days in between, and finally averages the difference.

/*
DESCRIPTION    Estimate Database growth based on backups.

Assuming backup size grows at the same rate as the Database size.  
First calculate difference in size between backups,
and then divides it by the number of days the backup took place
Finaly, averages the result.
CONFIGURATION    
    Set @LastXday to limit the number of days to search for
    Set @dbname for the database
 
Compatibility list:
MSSQL2005
MSSQL2008
MSSQL2012

 */ 
declare @dbname varchar(500)
declare @LastXdays nvarchar(2)
set @dbname = 'AdventureWorks'
set @LastXdays = '150'

;WITH BK_Growth (BKsize,BKDate,rownumber) as(  
	SELECT
		 backup_size
		,backup_start_date
		,row_number() OVER 
				(ORDER BY database_name,
				[type], backup_start_date DESC)
				AS rownumber
	FROM msdb.dbo.backupset
	WHERE
		database_name like @dbname
		and DATEDIFF(dd,([backup_finish_date]),GETDATE()) < @LastXdays
		and type = 'D'
)
select 
@dbname 'dbname'
,CAST( CAST(avg(100*((
(prev.BKSize - cur.BKSize)/cur.BKSize)/(DATEDIFF(dd,cur.BKDate,Prev.BKDate))
)) as NUMERIC(5,3))
as VARCHAR(5))+' %' 'Average Daily Growth'

,     (CAST(mfrows.RowSize AS FLOAT)*8)/1024 RowSizeMB
,     (CAST(mflog.LogSize AS FLOAT)*8)/1024 LogSizeMB
 
from BK_Growth cur
inner join BK_Growth prev on CUR.rownumber = (PREV.rownumber+1)

cross apply sys.databases db
    LEFT JOIN (
    SELECT database_id, SUM(size) RowSize 
    FROM sys.master_files 
    WHERE type = 0 and database_id = DB_ID(@DBName)
    GROUP BY database_id, type
        ) mfrows ON mfrows.database_id = db.database_id
    
    LEFT JOIN (
    SELECT database_id, SUM(size) LogSize 
    FROM sys.master_files 
    WHERE type = 1  and database_id = DB_ID(@DBName)
    GROUP BY database_id, type
        ) mflog ON mflog.database_id = db.database_id

WHERE mfrows.RowSize is not null
GROUP BY mfrows.RowSize, mflog.LogSize