Question

(PLZ NEED HELP) The doubling time of a bacterial population is 10 minutes. After 80 minutes, the bacterial population was 80000. _____

Using your rounded answer for the initial population above (do not round your growth rate), find the size of the bacterial population after 5 hours.____

Answer 1

Initial population = 313

Population after 5 hours =
`3.36 * 10^(11)`

Explanation:

Let initial population =
`x`

It is given that population gets doubled every 10 minutes.

Population after 10 minutes =
`2x`

Population after 20 minutes =
`2^(2) x`

:

:

Population after 80 minutes =
`2^(8) x` and it is given as 80000.

`\Rightarrow 2^(8) x = 80000\\\Rightarrow x = (80000)/(256)\\\Rightarrow x = 313`

So, initial population is 312.5 = ~313

To find, population after 5 hours i.e. 5
`*` 60 = 300 minutes

Population after 300 minutes =

`2^(30) x\\\Rightarrow 2^(30) * 313\\\Rightarrow 3.36 * 10^(11)`

So, the answers are:

Initial population = 313

Population after 5 hours =
`3.36 * 10^(11)`