I'd says that SEO traffic generally grows linearly with the number of external links, not exponentially. However, that is a gross oversimplification.
Not all links are created equal. Some links are orders of magnitude more important for SEO than others. Just counting links and not factoring in their power is going to give very poor correlation with SEO traffic compared to a metric that judges links according to their authority.
It is almost impossible to have exponential growth without a "viral" factor. Exponential traffic growth is almost always driven by people sharing your content with at least one other person (on average). Even for SEO traffic, exponential growth is often because of an exponential growth of inbound links. In other words, the more traffic you get from SEO, the more links you get because the same fraction of people create links.
While authority is a major search engine ranking factor, it is hardly the only one. It is a mistake not to encourage backlinks, but it is also a mistake to ignore the hundreds of other factor that go into SEO. There are bigger SEO returns when you focus on building a fantastic, usable, content-rich, crawlable, high-performance website compared to just managing backlinks.
SEO traffic growth doesn't come primarily from better rankings. A huge portion of new SEO traffic is new ranking for different phrases. Some of that comes from more authority. A site with more authority will be able to rank for a much wider variety of search phrases with the same content. However, much of that also comes from content development. If you create another 100 pages, you are likely to more than double your SEO traffic because your authority will increase while your keyword universe doubles.
