Answer:
The hourly growth rate is of 4.43%.
The function showing the number of bacteria after t hours is [tex]P(t) = 80(1.0443)^t[/tex]
Step-by-step explanation:
Equation of population growth:
The equation for the 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 growth rate, as a decimal.
The conditions are such that the number of bacteria is able to double every 16 hours.
This means that [tex]P(16) = 2P(0)[/tex]. We use this to find r.
[tex]P(t) = P(0)(1+r)^t[/tex]
[tex]2P(0) = P(0)(1+r)^{16}[/tex]
[tex](1+r)^{16} = 2[/tex]
[tex]\sqrt[16]{(1+r)^{16}} = \sqrt[16]{2}[/tex]
[tex]1 + r = 2^{\frac{1}{16}}[/tex]
[tex]1 + r = 1.0443[/tex]
[tex]r = 1.0443 - 1[/tex]
[tex]r = 0.0443[/tex]
The hourly growth rate is of 4.43%.
80 bacteria are placed in a petri dish.
This means that [tex]P(0) = 80[/tex].
[tex]P(t) = P(0)(1+r)^t[/tex]
[tex]P(t) = 80(1+0.0443)^t[/tex]
[tex]P(t) = 80(1.0443)^t[/tex]
The function showing the number of bacteria after t hours is [tex]P(t) = 80(1.0443)^t[/tex]
