I am a TA for complexity theory course. I want to explain the Exponential Time Hypothesis (ETH) to undergraduate students. They have done algorithm and theory of computation course. They know about SAT problem, with brute force algorithms to solve SAT. I have explained the ETH hypothesis in less than half hour.
One way is like this wikipedia
"The hypothesis states that $3$-SAT (or any of several related NP-complete problems) cannot be solved in subexponential time in the worst case". The exponential time hypothesis, if true, would imply that P ≠ NP, but it is a stronger statement. It can be used to show that many computational problems are equivalent in complexity,in the sense that if one of them has a subexponential time algorithm then they all do.
I then try to explain the each important point of the of definition. I don't this will be the right way. I want to convey the significance of the ETH.
Question : How to explain ETH to undergraduate students?