Q: RPMS rarely go past 3000 except pushing down hard on accelerator

Hello,

I just purchased this car used about two weeks ago. When first driving it I noticed how much more sensitive the accelerator was than my other old car 98 Chrysler concorde. I would put a little pressure, and would see the RPM jump up to around 4000-5000 range and then go back down to normal 2000-3000. This was frequent for the first week n half or so. I noticed two days ago though, the car does not want to go past 3000 rpms anymore, and at times I will push increasingly hard on the accelerator to have it go past it with no luck. If I really push the pedal down, it will go up to the 4000-6000 range but then back down. I've noticed a definite change and wanted to see if this seems like a major or lingering issue? No check engine lights are on or anything, oil and transmission fluid are both full. I would love some insight to this.

My car has 88500 miles.
My car has an automatic transmission.