The popping noises after your MTD riding tractor has been shut down are caused by the gas still being ignited without spark. This is usually caused by bad or old gas left in the riding tractor.
You should drain the old gas and replace it with fresh gas. Gas only stays fresh for about one month so if there is still gas in the tractor from last season it is definitely stale.
The tag that has the model and serial number of your MTD riding tractor can be found under the seat.
NOTE: if you need a part for the small engine in your MTD lawn tractor, there will be a separate model/serial number for the engine. Here are the small engines that are available in your MTD tractor. Visit the page of the engine you have to find out where the model/serial number is located for your small engine model: