To explain more, for e.g., we hear that the USD was backed by the convertibility of this currency to precious metals until 1971. Now, what are altcoins backed by such as Ethereum or Litecoin? Are mathematical calculations performed by ASIC miners any useful in the real world?
No they are not backed by calculations made by asic miners in the world.
Altcoins are backed by the project itself, the idea worth money and that is what we are willing to pay for.
People buy bitcoins because they want to buy something with it, they buy bitcoin because they feel the price will go up, people buy bitcoin because they want to send money to someone and it costs too much with western union. Basically bitcoin has utility that people are willing to pay for and that is why it has a price.
Ethereum is just like the same, people want to play games on dapp so they buy it, people want to use the blockchain to create ICO so they buy it (and fund the ICO) people want to use the blockchain to improve a identity government branch so they buy it. Basically all coins have some utility and their price reflects that utility for it or the support of people for that coin.
This best explains it all, altcoins and bitcoin are backed by the people or rather investor who has purchased and sold for various reasons
I think thats why the continuity in growth and development of crypto currency will continue