Answer:
The hourly growth rate parameter is of 4.74%
Step-by-step explanation:
Continuous growth model:
The continuous growth model for a population after t hours is given by:
[tex]P(t) = P(0)(1+r)^t[/tex]
In which P(0) is the initial population and r is the hourly growth rate parameter, as a decimal.
A sample of 1500 bacteria selected from this population reached the size of 1805 bacteria in four hours.
This means that [tex]P(0) = 1500, P(t) = 1805, t = 4[/tex]
Find the hourly growth rate parameter.
[tex]P(t) = P(0)(1+r)^t[/tex]
[tex]1805 = 1500(1+r)^4[/tex]
[tex](1+r)^4 = \frac{1805}{1500}[/tex]
[tex]\sqrt[4]{(1+r)^4} = \sqrt[4]{\frac{1805}{1500}}[/tex]
[tex]1 + r = (\frac{1805}{1500})^{\frac{1}{4}}[/tex]
[tex]1 + r = 1.0474[/tex]
[tex]r = 0.0474[/tex]
0.0474*100% = 4.74%
The hourly growth rate parameter is of 4.74%
