Question

The diameter of a bacteria colony that doubles every hour is represented by the graph below. What is the diameter of the bacteria after 8 hours?

graph of a curve passing through the points zero comma 1, one comma two, two comma four, and three comma eight


128
256
512
1,024

Answer 1

Option B: 256 is the diameter of the bacteria after 8 hours.

Step-by-step explanation:

From the given, it is obvious that the graph is an exponential function.

The general formula is given by,

`y=a(b)^x`

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,

`b=2`

Let us substitute the coordinate (0,1) and
`b=2`, we get,

`1=a(2)^0`

`1=a`

Thus, substituting
`a=1` and
`b=2` in the general formula
`y=a(b)^x`, we have,

`y=1(2)^x`

We need to determine the diameter of the bacteria after 8 hours.

Let us substitute x = 8 in the equation
`y=1(2)^x`, we get,

`y=1(2)^8`

`y=1(256)`

`y=256`

Thus, the diameter of the bacteria after 8 hours is 256

Hence, Option B is the correct answer.