Answer:
The hourly growth rate is of 3.15%
Step-by-step explanation:
The population of bacteria after t hours can be modeled by the following formula:
[tex]P(t) = P(0)e^{rt}[/tex]
In which P(0) is the initial population and r is the hourly growth parameter, as a decimal.
A sample of 3000 bacteria selected from this population reached the size of 3145 bacteria in one and a half hours. Find the hourly growth rate parameter.
This means that [tex]P(0) = 3000, P(1.5) = 3145[/tex]
We use this to find r.
[tex]P(t) = P(0)e^{rt}[/tex]
[tex]3145 = 3000e^{1.5r}[/tex]
[tex]e^{1.5r} = \frac{3145}{3000}[/tex]
[tex]\ln{e^{1.5r}} = \ln{\frac{3145}{3000}}[/tex]
[tex]1.5r = \ln{\frac{3145}{3000}}[/tex]
[tex]r = \frac{\ln{\frac{3145}{3000}}}{1.5}[/tex]
[tex]r = 0.0315[/tex]
The hourly growth rate is of 3.15%
