Answer :
We could state an exponential model.
Number of bateria will be given by:
[tex]N=N_0e^{kt}[/tex]where k=growth constant and t=time in minutes.
We're given that N0 is the initial population, which is:
[tex]N_0=9,085[/tex]We also know that, when t=236 min, N=2(9,085) = 18,170:
[tex]18,170=9,085e^{k(236)}^{}[/tex]We're going to solve this equation to find the value of k:
[tex]\begin{gathered} \frac{18,170}{9,085}=e^{236k} \\ 2=e^{236k} \\ \ln 2=\ln e^{236k} \\ \ln 2=236k \\ k=\frac{\ln 2}{236} \end{gathered}[/tex]Then, our expression is:
[tex]N=9,085e^{\frac{\ln 2}{236}t}[/tex]To find the population of bacteria after 708 minutes, we replace t by 708:
[tex]N=9085e^{\frac{\ln2}{236}(708)}=72680[/tex]Therefore, the population of bacteria 708 minutes from now, is 72680.
