Step 1 :The problem provides the function $P(t)=2.787(1.487)^{t}$, where $t$ is the number of years after 2004, to model the increase in millions of users on a social networking site.
Step 2 :We are asked to estimate the number of users of this site that could be online concurrently in 2005, 2009, and 2012. We can do this by substituting the appropriate values for $t$ into the function and rounding to the nearest million.
Step 3 :For 2005, $t$ would be 1. Substituting this into the function gives $P(1)=2.787(1.487)^{1} \approx 4$ million users.
Step 4 :For 2009, $t$ would be 5. Substituting this into the function gives $P(5)=2.787(1.487)^{5} \approx 20$ million users.
Step 5 :For 2012, $t$ would be 8. Substituting this into the function gives $P(8)=2.787(1.487)^{8} \approx 67$ million users.
Step 6 :Final Answer: The estimated number of users that could be online concurrently in 2005, 2009, and 2012 are approximately \(\boxed{4}\) million, \(\boxed{20}\) million, and \(\boxed{67}\) million respectively.