Rendering math, Fast Freddy and his best friend Sammy Snail decide to have a contest using their favorite video game. The player with the
greatest number of mouse clicks after two hours is the winner. Fast Freddy decides
to make the contest more difficult for himself by giving Sammy Snail an automatic
500 points and a 30 minute head start. If St is the number of mouse clicks made by
Sammy Snail after t minutes, and Ft is the number of mouse clicks made by Fast
Freddy after t minutes, then St is a transformation of Ft as given by
S(t)=23F(t+30)+500. The table shows the number of mouse clicks made by Fast
Freddy at 30 minute intervals after the beginning of the race, with the missing entry
due to the head start. How many mouse clicks were made by Sammy Snail after 90
minutes?