Answer:
The size of the population after 9 hours is 880 bacterias.
Step-by-step explanation:
The population of the bacteria after t hours is given by the following equation:
[tex]P(t) = P_{0}(1+r)^{t}[/tex]
In which [tex]P_{0}[/tex] is the initial population and r is the growth rate.
Suppose there are initially 110 bacteria.
This means that [tex]P_{0} = 110[/tex].
Under ideal conditions a certain bacteria population is known to double every three hours.
This means that [tex]P(3) = 3*110 = 330[/tex]
So
[tex]P(t) = P_{0}(1+r)^{t}[/tex]
[tex]220 = 110(1+r)^{3}[/tex]
[tex](1+r)^{3} = 2[/tex]
Applying the cubic root to both sides
[tex]1 + r = 1.26[/tex]
[tex]r = 0.26[/tex]
So
[tex]P(t) = 110(26)^{t}[/tex]
What is the size of the population after 9 hours
This is P(9)
[tex]P(t) = 110(1.26)^{9} = 880[/tex]
The size of the population after 9 hours is 880 bacterias.
