Problem $2$: In a manufacturing plant that makes cell phone sim cards defects are treated by running the sim card through a machine that runs a short repair routine. The machine takes exactly $2$ minutes to repair each sim card. The plant manager noticed that defects occurred randomly and decided to do a time study. They discovered that the average time in between the occurrence of defects was $2\mathrm{.}5$ minutes and that the time in between defects was exponentially distributed. What is the average number of sim cards at the repair machine? The plan manager estimates that sim cards depreciate at $25$ cents per minute.

What type of model is appropriate? $($M$/$M$/1,$ M$/$D$/1,$ M$/$M$/$c$,$ or PK formula$)$