How to check the growth of database
You can query the default trace to get information about recent growth events.

DECLARE @path nvarchar(260) = (
    SELECT REVERSE(SUBSTRING(REVERSE(path), CHARINDEX('\', REVERSE(path)), 260)) +'log.trc'
    FROM    sys.traces
    WHERE   is_default = 1)

SELECT gt.DatabaseID,
       gt.FileName,
       COUNT(*) AS NumberOfEvents,
       CASE WHEN te.name LIKE'%Grow' THEN 1 ELSE 0 END AS is_growth_event
FROM  sys.fn_trace_gettable(@path, DEFAULT) gt
JOIN sys.trace_events te ON gt.EventClass = te.trace_event_id
WHERE   te.name in ('Data File Auto Grow','Log File Auto Grow','Data File Auto Shrink','Log File Auto Shrink')
GROUP BY gt.DatabaseID,
       gt.FileName,
       te.name


You can also use Event Notifications to be notified on DATA_FILE_AUTO_GROW,LOG_FILE_AUTO_GROW without having to poll the trace.