As the colony doubles every hour, the population \(p\) is modeled by:
\(p = 2^t\)
Where \(t\) is the time in hours.
We can see this because:
\(2^0 = 1 \\ 2^1 = 2 \\ 2^2 = 4\)
Notice that the x coordinate of the graph corresponds to the time, and the y coordinate corresponds to the population.
Thus at \(t=9\)
\(p=2^9 \\ \\ p = \boxed{512}\)
