A new social networking site plans to go live with 5,000 beta testers already having user profiles.

At first, the site's marketing team expects the number of user profiles on the site to double every two months, as represented by the function f, which is graphed below.

When the number of user profiles reaches 40,000, the marketing team will launch an advertising campaign to introduce premium profiles, and a different function will be used to model the expected number of user profiles on the site.

The function f represents the marketing team's expected number of user profiles after x months, when the domain is restricted to all numbers on the interval .