From the statement of the problem, we know that:
• the initial population of bacteria in a colony is N_0 = 500,
,• the number of bacteria doubles every △t = 260 min.
We can model the population of bacterias in the colony by the exponential function:
[tex]N(t)=N_0\cdot r^{t/\Delta t}=500\cdot2^{t/260\min .}[/tex]After a time t = 520 min, the population will be:
[tex]N(520\min )=500\cdot2^{520\min /260\min }=500\cdot2^2=500\cdot4=2000.[/tex]Answer
After 520 minutes, the population will be 2000 bacterias.
