Is the Universe 10,000 Billion Years Old?

If Neil deGrasse Tyson tells me the universe is 15 billion years old, I'm gonna take basically on faith that he's right. In any universe with infinite time, why not? How are we supposed to live in a world where one of the tenets of rationality is, if you have doubt, you move to resolve it? That is the purpose of doubt. And also we don't have infinite time, we don’t have infinite energy.