Please see this Usage Note under like:
(I have made the relevant section red.)
The use of like to mean such as was formerly thought to be undesirable in formal writing, but has now become acceptable. It was also thought that as rather than like should be used to mean in the same way that, but now both as and like are acceptable: they hunt and catch fish as/like their ancestors used to. The use of look like and seem like before a clause, although very common, is thought by many people to be incorrect or non-standard: it looks as though he won't come (not it looks like he won't come)
That is, once the use of 'like' in the sentence above would have a been considered an error. Some people still hold to this rule. Now, many people would accept either one in the topic sentence.
If you are doing this for classwork, your teacher may be someone who thinks only 'as' should be used in this sentence.