That sounds pretty typical; I don't think that there's anything wrong. What's going on: at 6 PM, everything in the apartment is maybe 75 degrees. (Probably never got all the way up to 79.) The humidity is up, too, unless your apartment is sealed up tight and you didn't leave any damp towels out and don't have any plants.
You turn the AC down to 71, and it starts running. You don't see much temperature change at first, but the AC is pulling moisture out of the air, so you're feeling more comfortable as the humidity drops. The air temperature starts coming down after maybe 30 - 45 minutes of run time, but, even though the air is getting cooler, there's a lot of heat stored up in your walls and furniture that's got to flow out to the air before the AC can remove it.
So, it takes awhile. By 8, the air temperature is down to 71, but heat is still coming from the walls and furniture, so the air warms back up and the AC comes back on after 5 minutes. This is pretty normal if you're trying to save energy and money by turning up the thermostat while your at work.
Life is full of compromises. You might consider installing a programmable thermostat, so you can turn the AC on sometime around 5, as a compromise between comfort and saving energy.
Its normal...being that your apartment is hot,it will take some time for the a/c to cool the house. Set you a/c on 75° and notice the difference.
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