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
[tex]y=100(2)^{(\frac{t}{6.5})}[/tex]where
x is the number of hours
y is the total bacteria
so
For a day -------> t=24 hours
substitute
[tex]\begin{gathered} y=100(2)^{(\frac{24}{6.5})} \\ y=1,293\text{ bacteria} \end{gathered}[/tex]For a half day -------> t=12 hours
substitute
[tex]\begin{gathered} y=100(2)^{(\frac{12}{6.5})} \\ y=360\text{ bacteria} \end{gathered}[/tex]For a day and a half -------> t=36 hours
substitute
[tex]\begin{gathered} y=100(2)^{(\frac{36}{6.5})} \\ y=4,648\text{ bacteria} \end{gathered}[/tex]
