Answer
See below.
Work Step by Step
Proofs using mathematical induction consists of two steps:
1) The base case: here we prove that the statement holds for the first natural number.
2) The inductive step: assume the statement is true for some arbitrary natural number $n$ larger than the first natural number, then we prove that then the statement also holds for $n + 1$.
Hence here: 1) For $n=3: 3^2=9\gt2\cdot3+1=7$
2) Assume for $n=k: k^2\gt2k+1$.
Then for $n=k+1$: $(k+1)^2=k^2+2k+1\gt2+2k+1=2k+3=2(k+1)+1$ because $k^2\gt2$ because $k\geq3$
Thus we proved what we wanted to.