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.

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.