Question

A culture started with 5000 bacteria after 5 hours it grew to 6500 bacteria predict how many bacteria will be present after 16 hours

Answer 1

After 16 hours bacterial count will be 11600.

Explanation:

Bacterial growth is always an exponential growth in a given culture.So the formula for the growth will be

Final counts of bacteria = Initial counts ×
`(rate of growth)^(time)`

Given from first part Initial counts = 5000

Final counts= 6500 and time of growth = 5 hours

Then we will get the value of rate of growth of bacteria from the bacteria

⇒ 6500 = 5000×
`(rate)^(5)`

`(rate)^(5)= (6500)/(5000) = 1.3`

`Rate = \sqrt[5]{1.3} = 1.05`

Now again to get the value of bacteria after 16 hours

Final Count = 5000×
`(1.05)^(16)`

= 5000×2.32

= 11600