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}`