Question

A scientist counted 24 bacteria present in a culture and finds that the number of bacteria doubles each hour. Which of the following analytical models illustrates this situation?

Answer 1

We can call the moment when the scientist found the 24 bacteria x=0.

After one hour (x=1) there will be 48 bacteria, since they duble each hour.

After two hours (x=2) there will be 96 bacteria.

After three hours (x=3) there will be 192 bacteria.

We can rewrite these numbers as follows:

`24=24\cdot1=24\cdot2^0`
`48=24\cdot2=24\cdot2^1`
`96=24\cdot4=24\cdot2^2`
`192=24\cdot8=24\cdot2^3`

Thus, the best model for this behaviour is

`y=24(2)^x^{}`