Explain why an amplified analog signal will have deteriorated compared with the origional signal?

Well, yes they do. Any amplification adds noise to the signal. Some of this can be removed but the effects are cumulative. Imagine making a copy of a piece of music by an analog technique. Then making a copy from that copy, etc. You get more and more noise added to the system, even when the amplification is one. In digital systems, the music (or whatever) is made of bits that are either there or not. Cleaning up the bits is very easy. Perfect copies are typical.