Does the recovery model affect growth of the .mdf file? On my production database, the .mdf file is rapidly growing on a daily basis.

If I change the recovery model from SIMPLE to FULL, will that help?
the simple recovery model only affects the log files of your database (.ldf).

If your datafiles are growing, you can check the tables that are occupying more space, you can use the management studio: right click on the database> reports > standard reports > disk usage by top tables

this way you can determine which table is taking all the space and plan a cleanup task for that (or move data to another DB)