Answer:
[tex]P(t) = 2000e^{-0.23t}[/tex]
Step-by-step explanation:
The exponential formula for the size of the bacteria population after t hours is given by:
[tex]P(t) = P_{0}e^{rt}[/tex]
In which [tex]P_{0}[/tex] is the initial population and r is the rate which the population changes.
A population of bacteria is initially 2,000.
This means that [tex]P_{0} = 2000[/tex]
After three hours the population is 1,000.
This means that [tex]P(3) = 1000[/tex]
So
[tex]P(t) = P_{0}e^{rt}[/tex]
[tex]1000 = 2000e^{3r}[/tex]
[tex]e^{3r} = 0.5[/tex]
[tex]\ln{e^{3r}} = \ln{0.5}[/tex]
[tex]3r = -0.69[/tex]
[tex]r = \frac{-0.69}{3}[/tex]
[tex]r = -0.23[/tex]
Find the exponential function that represents the size of the bacteria population after t hours.
[tex]P(t) = 2000e^{-0.23t}[/tex]
