In this Purchase Path the consumer sees the banner impression, 10 days go by, and then they do a search and click on the sponsored link.
a) In this attribution rule, you think that a banner cannot last in a consumers mind for 10 days and therefore the entire sale is attributed to the search.
b) In this attribution rule, you believe the banner impression is responsible for some portion of the sale and had some influence on the consumer. The search term also deserves some portion of credit for the conversion. It is therefore concluded that a banner can influence a consumer 10 days after being seen.