Question

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? (0,1) (1,2) (2,4) (3,8)

Answers:
128
256
512
1024

Answer 1

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 $t=9$

$p=2^9 \\ \\ p = \boxed{512}$