Answer:
a) P(24) = 1025.
b) P(24) = 191.
Step-by-step explanation:
This population can be modeled by the following exponential model.
[tex]P(t) = P_{0}e^{rt}[/tex]
In which P(t) is the population after t hours, [tex]P_{0}[/tex] is the initial population and r is the decimal growth rate.
The initial number of bacteria in the culture is 28. This means that [tex]P_{0} = 28[/tex].
Population after 24 hours.
(a) No antibiotic is present, so the relative growth rate is 15%.
So r = 0.15.
[tex]P(t) = P_{0}e^{rt}[/tex]
[tex]P(24) = 28e^{0.15*24} = 1024.75[/tex]
(b) An antibiotic is present in the culture, so the relative growth rate is reduced to 8%.
So r = 0.08.
[tex]P(t) = P_{0}e^{rt}[/tex]
[tex]P(24) = 28e^{0.08*24} = 190.99[/tex]
