Answer:
The size of the sample after four hours is of 3158 bacteria.
Step-by-step explanation:
The population after t hours can be modeled by the continuous exponential growth model, which is:
[tex]P(t) = P(0)e^{rt}[/tex]
In which P(0) is the initial population and r is the growth rate paremeter.
A growth rate parameter of 17% per hour.
This means that [tex]r = 0.17[/tex]
Suppose also that a sample culture of 1600 is obtained from this population.
This means that [tex]P(0) = 1600[/tex]
Find the size of the sample after four hours.
This is P(4).
[tex]P(t) = P(0)e^{rt}[/tex]
[tex]P(t) = 1600e^{0.17t}[/tex]
[tex]P(4) = 1600e^{0.17*4}[/tex]
[tex]P(4) = 3158.2[/tex]
Rounding to the nearest integer
The size of the sample after four hours is of 3158 bacteria.
