Step 1 :The problem asks for the number of users that could be online concurrently in 2003. We can use the given function \(P(t)=2.575(1.487)^{t}\) to calculate this. The variable \(t\) represents the number of years after 2002, so for 2003, \(t=1\).
Step 2 :Substitute \(t=1\) into the function, we get \(P(1)=2.575(1.487)^{1}\).
Step 3 :Calculate the value of \(P(1)\), we get \(P(1) = 3.8290250000000006\).
Step 4 :Round \(P(1)\) to the nearest whole number, we get \(P(1) = 4\).
Step 5 :Final Answer: The number of users of this site that could be online concurrently in 2003 is approximately \(\boxed{4}\) million.