Answer:
[tex]P (t) = 580e ^ {0.18t}[/tex] or [tex]P (t) = 580 (1.18) ^ t[/tex]
Step-by-step explanation:
There are two models of exponential growth that you can use to predict the population of bacteria after t hours.
I) [tex]P (t) = pe ^ {rt}[/tex]
II) [tex]P (t) = p (1 + r) ^ t[/tex]
Where
p is the initial population of bacteria
r is the growth rate
t is the time in hours.
In this case we know that:
[tex]p = 580\\\\r = \frac{18}{100}\\\\r = 0.18[/tex]
Then the equations that can be used to predict the population of bacteria after t hours are:
I) [tex]P (t) = 580e ^ {0.18t}[/tex]
II)[tex]P (t) = 580 (1 + 0.18) ^ t[/tex]
