Answer:
2.71 hours are required for the number of bacterias grouper are tripled.
Step-by-step explanation:
The number of bacterias can be given by the following exponential function:
[tex]N(t) = N_{0}e^{rt}[/tex]
In which [tex]N(t)[/tex] is the number of bacterias at the time instant t, [tex]N_{0}[/tex] is the initial number of bacterias and r is the rate for which they grow.
After 1 hour the crop has reached ( 3/2 ) N₀ Bacterias.
This means that [tex]N(1) = 1.5N_{0}[/tex]. With this information, we can find r.
[tex]N(t) = N_{0}e^{rt}[/tex]
[tex]1.5N_{0} = N_{0}e^{r}[/tex]
[tex]e^{r} = 1.5[/tex]
To find r, we apply ln to both sides
[tex]\ln{e^{r}} = \ln{1.5}[/tex]
[tex]r = 0.405[/tex]
Determine the time required for the number of bacterias grouper are tripled.
This is t when [tex]N(t) = 3N_{0}[/tex]
[tex]N(t) = N_{0}e^{0.405t}[/tex]
[tex]3N_{0} = N_{0}e^{0.405t}[/tex]
[tex]e^{0.405t} = 3[/tex]
Again, we apply ln to both sides
[tex]\ln{e^{0.405t}} = \ln{3}[/tex]
[tex]0.405t = 1.10[/tex]
[tex]t = 2.71[/tex]
2.71 hours are required for the number of bacterias grouper are tripled.
