Question

A certain type of bacteria, given favorable growth medium, quadruples in population every 6 hours. Given that there were 150 bacteria to start with, how many bacteria will there be in two and a half days?

Answer 1

157,286,400 bacteria.

Explanation:

We have been given that a certain type of bacteria, given favorable growth medium, quadruples in population every 6 hours. Given that there were 150 bacteria to start with.

We will use exponential growth function to solve our given problem.

`y=a\cdot b^x}`, where

y = Final value,

a = Initial value,

b = Growth factor.

x = Time.

Quadruples meaning 4 at a time, so growth factor is 4.

We are also told that population becomes 4 times every 6 hours, so time would be
`(1)/(6)x`.

Initial value is given as 150.

Upon substituting these values in above formula, we will get:

`y=150(4)^{(1)/(6)x}`

Let us convert two and a half days into hours.

1 day = 24 hours.

2.5 days = 2.5*24 hours = 60 hours.

To find the bacteria population in two and half days, we will substitute
`x=60` in our formula as:

`y=150(4)^{(1)/(6)(60)}`

`y=150(4)^(10)`

`y=150(1048576)`

`y=157,286,400`

Therefore, there will be 157,286,400 bacteria in two and a half days.