Option B: 256 is the diameter of the bacteria after 8 hours.
Explanation:
From the given, it is obvious that the graph is an exponential function.
The general formula is given by,
[tex]y=a(b)^x[/tex]
Where a is the initial population,
b is the growth rate and
x is the number of hours.
It is given that the diameter of the bacteria doubles every hour.
Then, we have,
[tex]b=2[/tex]
Let us substitute the coordinate (0,1) and [tex]b=2[/tex], we get,
[tex]1=a(2)^0[/tex]
[tex]1=a[/tex]
Thus, substituting [tex]a=1[/tex] and [tex]b=2[/tex] in the general formula [tex]y=a(b)^x[/tex], we have,
[tex]y=1(2)^x[/tex]
We need to determine the diameter of the bacteria after 8 hours.
Let us substitute x = 8 in the equation [tex]y=1(2)^x[/tex], we get,
[tex]y=1(2)^8[/tex]
[tex]y=1(256)[/tex]
[tex]y=256[/tex]
Thus, the diameter of the bacteria after 8 hours is 256
Hence, Option B is the correct answer.
