Answer:
[tex]P = 6099\ bacterias[/tex]
Step-by-step explanation:
We must use the exponential growth formula:
[tex]P = be ^ {rt}[/tex]
Where
P is the population of bacteria as a function of time
b is the initial population of bacteria.
r is the growth rate
t is the time in hours
We know that the initial amount of bacteria is 2000. Then [tex]b = 2000[/tex]
Then
[tex]P = 2000e ^ {rt}[/tex]
After t = 4 hours the population P was 2600. Then we substitute these values in the equation and solve for r.
[tex]P = 2600 = 2000e^{4r}[/tex]
[tex]\frac{2600}{2000} = e ^ {4r}[/tex]
[tex]1.3 = e ^ {4r}\\\\ln (1.3) = ln (e ^ {4r})\\\\ln (1.3) = 4r\\\\r = \frac{ln (1.3)}{4}\\\\r = 0.06559[/tex]
Now we can write the equation for this problem as:
[tex]P = 2000e ^{0.06559t}[/tex]
For t = 17 hours the amount of bacteria will be:
[tex]P = 2000e ^{0.06559 (17)}[/tex]
[tex]P = 6099\ bacterias[/tex]
