We know that the exponential growth of the Bacteria's population is model by the function [tex]f(x)=100(4)^x[/tex], so to find the number of bacteria after 6 hours, we just need to evaluate our function at [tex]x=6[/tex]. In other words, we are going to replace [tex]x[/tex] with 6 in our function:
[tex]f(x)=100(4)^x[/tex]
[tex]f(6)=100(4)^6[/tex]
[tex]f(6)=409600[/tex]
We can conclude that the we should use the equation: [tex]f(6)=100(4)^6[/tex] to find the number of bacteria in the colony after 6 hours. Evaluating the function we get that the number is 409,600.
