Authoritative appeal refers to a statement that uses authority to defend a position or convince someone, this implies the position, knowledge or power of someone is used as part of the argument, this type of argument is usually considered as invalid as it does not focus on the evidence but rather on the reputation of someone. In the case of "Representative Lee has 15 years of experience in promoting the rights of small businesses." it is appealing to the authority as it refers to Representative Lee experience and this information is probably used as part of an argument that suggest Representative Lee is an expert on promoting the rights or small victims and because of this can said or do certain things, which might not be true.
It looks perfectly fine the answer is well said and has supporting sentences to prove your statement. Wording is a little of where you said "but shows even more in the second half." It's not that big of a deal but just kind of rolls of the tongue weirdly not a necessary change but just thought I'd point it out.
