Answer:
[tex]P(t) = 10058\ bacterias[/tex]
Step-by-step explanation:
To perform this calculation we must use the exponential growth formula
The exponential growth formula is
[tex]P(t) = Ae^{kt}[/tex]
Where
A is the main coefficient and represents the initial population of bacteria
e is the base
k is the growth rate
t is time in hours.
Let's call t = 0 to the initial hour.
At t = 0 the population of bacteria was 6000
Therefore we know that:
[tex]P(0) = 6000[/tex] bacteria
After t = 6 hours, the population of bacteria was 7200
Then [tex]P(6) = 7200[/tex] .
Now we use this data to find the variables a, and k.
[tex]P(0) = 6000 =Ae ^{k(0)}\\\\6000 = A(e ^ 0)\\\\A = 6000[/tex].
Then:
[tex]P(6) = 6000e^{k(6)}\\\\7200 = 6000e ^{6k}\\\\\frac{7200}{6000} = e^{6k}\\\\ln(\frac{7200}{6000}) = 6k\\\\k = \frac{ln(\frac{7200}{6000})}{6}\\\\k =0.03039[/tex]
Finally the function is:
[tex]P(t) = 6000e^{0.03039t}[/tex]
After 17 hours:
[tex]t = 17 hours[/tex]
So the population of bacteria after t=17 hours is:
[tex]P(t) = 6000e^{0.03039(17)}[/tex]
[tex]P(t) = 10058\ bacterias[/tex]
Answer:
r=0.03
A=9,991.7
Step-by-step explanation:
We will use the following formula to find the rate of growth:
[tex] A = p e^{ r t } [/tex]
Here, [tex] A = 7200 [/tex]
[tex] P = 6000 [/tex]
[tex] T= 6 hours [/tex]
[tex]r=\frac{\frac{log\frac{a}{p} }{log e} }{t}[/tex]
[tex]r=\frac{\frac{log\frac{7200}{6000} }{log e} }{6}[/tex]
r=0.03
Now we will predict how many bacteria will be present after 17 hours using the same formula:
[tex]A=p e^{rt}[/tex]
[tex]A=6,000 \times e^{(0.03\times 17)}[/tex]
A=9,991.7
