The diameter of a bacteria colony that doubles every hour is represented by the graph below. What is the diameter of the bacteria after 9 hours?

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=512