Answer:
[tex]\frac{log(6400)}{log(4)}[/tex]
Step-by-step explanation:
The initial population of bacteria is 800 and we know that this number is quadrupling every hour.
We're going to find a function in terms of t (time) that gives us the population of bacteria at that time.
Since the population is quadrupling every hour the function in terms of t (where t is expressed in hours) is:
[tex]f(t)=800(4^{t})[/tex]
Now we need to find the time when there will be 5,120,000 bacterias. This means the time t when f(t) = 5,120,000
So we have 5,120,000 = [tex]800(4^{t})[/tex]
[tex]5,120,000 = 800(4^{t})\\\frac{5,120,000}{800} =4^{t} \\6400=4^{t} \\log(6400) =t log(4)\\\frac{log(6400)}{log(4)} =t[/tex]
Therefore, the time when there will be 5,120,000 bacterias will be:
[tex]\frac{log(6400)}{log(4)}[/tex]
