Question

The doubling period of a bacterial population is 15 minutes. At time t =110 minutes, the bacterial population was 80000. What was the initial population at time t = 0? AND Find the size of the bacterial population after 5 hours.

Answer 1

Initial population was 496 to the nearest whole number

After 5 hours the population was 520169577 nearest whole number

Explanation:

The bacterial population count be `p`

For 1 growth cycle we have: `2xxp ->2^1p`
For 2 growth cycles we have `2xx2xxp->2^2p`

For `n` growth cycles we have `2^np`

Let time in minutes be `t`

The count of population cycles is: `2^(t/15)p`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Initial condition: `2^(110/15)p=80,000`

`color(blue)("Determine initial population count "->p)`

`p=80,000-:2^(22/3)`

`p=496.06282.......`

Initial population was 496 to the nearest whole number
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Determine population after 5 hours")`

`2^((5xx60)/15)p = 2^(20)p=520169576.709`

5 hours population size `=520169577` to the nearest whole number

`p_5=520169577`