Question

At the beginning of an experiement, there are 100 bacteria in a certain culture. If the number of bacteria doubles every hour, how many bacteria will be in the culture at the end of 6 hours? A. 200 b. 600 c. 3200 d. 6400

Answer 1

See explanation below

Explanation:

We have `100=B_0` bacteria at the begining in `t=0`
In `t=1`, we will have `2·B_0`
In `t=2` we will have `2·2·B_0` and so on

In `t=n` hours we will have `2^nB_0`

We call `B_n` to number of bacteria at n hours from begining. Then `B_n=2^nB_0` is the general term

At 6 hours we will have `B_6=2^6B_0=64·100=6400`