Question

suppose a single bacterium is placed in a bottle at 11:00 am. it grows and at 11:01 divides into two bacteria. these two bacteria each grow and at 11:02 divide into four bacteria, which grow and at 11:03 divide into eight bacteria, and so on. now, suppose the bacteria continue to double every minute and the bottle is full at 12:00.

how many bacteria are in the bottle at 11:39? what fraction of the bottle is full at that time?

there will be \\(2^{39}\\) bacteria in the bottle at 11:39.
(type your answer using exponential notation.)

the bottle will be full at that time.
(type an integer or a simplified fraction.)

Explanation:

Model the bacterial growth

Using the Bacterial Growth Modeling and Exponential Growth knowledge points

$$
LATEXBLOCK0
$$

Calculate bacteria at 11:39

Using the Exponential Growth knowledge point

$$
LATEXBLOCK1
$$

Determine the bottle capacity

Using the Exponential Growth knowledge point

$$
LATEXBLOCK2
$$

Calculate the fraction full at 11:39

Using the Exponential Growth knowledge point

$$
LATEXBLOCK3
$$

Answer:

Question 1

There will be \(2^{39}\) bacteria in the bottle at 11:39.

Question 2

The bottle will be \(\frac{1}{2097152}\) full at that time.