Question

A certain type of bacteria,given a favorable growthMedium, doubles in population every 6.5 hours. Given that there were approximately 100 bacteria to start with, how many bacteria will there be in a day and a half?

Answer 1

A certain type of bacteria,

given a favorable growth

Medium, doubles in population every 6.5 hours. Given that there were approximately 100 bacteria to start with, how many bacteria will there be in a day and a half?

we have that

the exponential growth function that represent this situation is

`y=100(2)^{((t)/(6.5))}`

where

x is the number of hours

y is the total bacteria

so

For a day -------> t=24 hours

substitute

`\begin{gathered} y=100(2)^{((24)/(6.5))} \\ y=1,293\text{ bacteria} \end{gathered}`

For a half day -------> t=12 hours

substitute

`\begin{gathered} y=100(2)^{((12)/(6.5))} \\ y=360\text{ bacteria} \end{gathered}`

For a day and a half -------> t=36 hours

substitute

`\begin{gathered} y=100(2)^{((36)/(6.5))} \\ y=4,648\text{ bacteria} \end{gathered}`