Respuesta :
Since each nine days the population doubles that means that after nine days we will have:
[tex]600[/tex]after 18 days we will have:
[tex]1200[/tex]and so on.
This means that we can model the population by a function of the form:
[tex]y=A\cdot B^x[/tex]where A is the inital population and B is the growth.
Now we know that the initial population is 300 and that it doubles each nine days, that means that B has to be two. To correctly model the population we need to make sure that this happens every nine days that means that the x should be divided by nine; therefore the function modeling the population is:
[tex]y=300(2)^{\frac{x}{9}}[/tex]where x represents the days.
Once we know the function we just plug the value we need, in this case we need the population after 26 days, this means that x=26, then we have:
[tex]\begin{gathered} y=300(2)^{\frac{26}{9}} \\ y=2222.1 \end{gathered}[/tex]Therefore we conclude that the population of bees after 26 days is approximatey 2222
