Answer:
[tex]3,462\ bacteria[/tex]
Step-by-step explanation:
In this problem we have a exponential function of the form
[tex]y=a(b^x)[/tex]
where
x is the time in hours
y is the numbers of bacteria
a is the initial value
b is the base
r is the rate of growth
b=(1+r)
we have that
[tex]a=3,000\ bacteria[/tex]
For x=8, y=3,300
substitute in the exponential function
[tex]3,300=3,000(b^8)[/tex]
solve for b
[tex]1.1=(b^8)[/tex]
[tex]b=\sqrt[8]{1.1}[/tex]
[tex]b=1.0120[/tex]
Find the value of r
[tex]r=b-1=1.0120-1=0.0120=1.20\%[/tex]
The equation is equal to
[tex]y=3,000(1.012^x)[/tex]
For x=12 hours
substitute the value of x in the equation
[tex]y=3,000(1.012^{12})[/tex]
[tex]y=3,462\ bacteria[/tex]
