Let $f(x)=a x^{2}+b x+c$, where $a, b$, and $c$ are integers. Suppose that $f(1)=0,50\textless f(7)\textless60,70\textless f(8)\textless80$, $5000 k\textless f(100)\textless5000(k+1)$ for some integer $k$. What is $k$? (2011 AMC 12A Problems, Question 20) 
选项为:A:$$1$$  B:$$2$$  C:$$3$$  D:$$4$$  E:$$5$$  请回答其中一个选项.