1. The problem statement, all variables and given/known data Prove that 3^n>n^4 for all n in N , n>=8 2. Relevant equations 3. The attempt at a solution Base case: 3^8>8^4 Inductive step Assume 3^n>n^4. Show 3^n+1>(n+1)^4 I tried a lot of approaches to get from the inductive hypothesis to what I want to show Ex: 3^n>n^4 3^n+1>3n^4 3n^4>(3n^4)-3=3(n^4-1)=3((n^2)-1)((n^2)+1)=3(n+1)(n-1)(n^2+1)>3(n+1)(n-1)(n^2-1) =3(n+1)(n-1)(n+1)(n-1)=3((n+1)^4-(n-1)^4) It looks like I went too far My other approach is this. It looks a little bit crazy, but I think it works 3^n+1>n^4+2*3^n I will show that n^4+2*3^n grows faster than (n+1)^4 by using limits and loopitals rule.