What drives long duration US Treasury Bond ETF prices?

I am looking at TLT, for example, a long duration (with average maturity around 25 years) bond ETF. I noticed that the fed funds rate (or the "interest rate" from federal reserve) has been very close to 0% both times around 2011 and today (2020). See chart here. However, the price of TLT has nearly doubled since 2011. I also noticed that even the 30-year yield has been similar in December 2008 as May/June 2019. The 30-year-yield was around 2.6% for both time periods; however, the price of TLT has risen a lot since 2008.

My question is: If both years had similar interest rates, what accounts for such massive price difference?

Follow up questions:

• It is understandable that short duration bond funds behave inversely mirroring fed funds rate; however, why are long-duration bond funds magnified by many multiples?? (for example, see SHY for example of a short duration ETF that only gained a few % in the same time period).
• Is this due to inflation? For example, interest rates were also near 0% right after the massive 1929 market crash. Yet, prices back then were far lower. Is TLT today is the same as what a 1929 TLT (had it existed back then) would have been, but just adjusted for inflation?
• Does this mean that even if fed funds rate stays at 0% forever, TLT will still just keep climbing?
• Conversely, Suppose we go back to 1979 insanely high rates, would there be a predictable pattern on HOW TLT drops? (for example, let’s say we raise interest rates 4% a year until we get to 20%. would TLT drop by a predictable X% per year to match that inverse?)