It's called a worst case scenario. Not a definite claim -
3,105 new cases on 15 September. If cases were to rise exponentially – leading to four “doublings” between now and mid-October – there would be 49,680 new cases on 13 October.
And your fact number 2, the fact is exactly the opposite. No one knows if there is a lasting immunity and the fear is that it doesn't last that long at all.
RE: Checking Gov COVID Logic/Maths - How Many Years Will it Take Before COVID19 is Over In Britain?