One rat found in house, what do I do?

[Josh Pass]

I just rented my first rental home 3 days ago. They found a rat in the house and freaked out bad. What do I have to do as a landlord?  Like legally? I obviously don't want a rat in there. The tenants are acting its the devil himself. Refuse to set foot at the property. A rat trap was put out at night and it didn't catch it that night. They then called in the morning demanding an exterminator. I called back less than an hour later and they had already called one to come by stating I took too long to respond. . . 

Anyways, I want to tread lightly here as I don't want to get sued or fined or something. Would this be considered an emergency issue? If so, what is the time frame I have to respond and then also take care of it? And what does taking care of it mean exactly? Just getting rid of the rat that's there or also doing things like plugging ANY holes that the exterminator deems should be fixed? Keep in mind, it's a 70 year house. I am charging less rent than anybody else in the area (if that matters ). I lived in that house for 5 years with no issue. It probably got in the one month it was vacant. 

I'm in Washington state if that makes a difference. 

This is the Thanks I get for trying to do property management myself I guess. . .