Linear Growth Rate of User Base

A mobile app company had an initial user base of 3000 users. They projected that their user base would grow linearly over time. After 12 months, they expect the user base to increase to 6000 users.

Let

$$ u(t) = ut + b $$

represent the number of users in the app at time $$ t $$ months, where $$ u(t) $$ is the total user count, $$ u $$ is the rate of increase per month, and $$ b $$ is the initial user base. Based on the data provided, find the value of $$ u $$ and input your answer as a simplified fraction.