Question

What was the initial population at time t=0? Find the size of the bacterial population after 3 hours.

Answer 1

We need to follow the formula to find the size of the bacterial population is,

`y=a(b)^t`

Here, t is the total amount of bacteria, a is the initial bacteria at time = 0, abd b is the growth factor ( which is 2 according to the question )

At t = 110 mins , y = 60,000 we have

`60,000=a(2)^{(110)/(15)}`
`\begin{gathered} a=(60000)/(2^(7.33)) \\ a=372.92 \end{gathered}`

Now, the size of the population after 3 hours

`2^{(3*60)/(15)}p=2^(12)p`
`\begin{gathered} 2^(12)*372.92=4096*372.92 \\ =1,527,480.32 \end{gathered}`

The answer is 1,527,480.32