Using exponential function concepts, it is found that the change of the growth factor of the population each half hour is given by:
b. [tex]\sqrt{\frac{1}{6}}[/tex]
e. [tex]\left(\frac{1}{6}\right)^{0.5}[/tex]
What is an exponential function?
An increasing exponential function is modeled by:
[tex]A(t) = A(0)(1 + r)^t[/tex]
In which:
- A(0) is the initial value.
- r is the decay rate, as a decimal.
In this problem, the growth factor of 1/6 each hour, hence, [tex]r = \frac{1}{6}[/tex], and:
[tex]A(t) = A(0)(1 + \frac{1}{6})^t[/tex]
For each half-hour, t = 0.5, hence the growth factor is of:
[tex]\left(\frac{1}{6}\right)^{0.5} = \sqrt{\frac{1}{6}}[/tex]
Hence, options b and e are correct.
You can learn more about exponential functions at https://brainly.com/question/25537936
