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 11:56? what fraction of the bottle is full at that time?

there will be \\(2^{56}\\) bacteria in the bottle at 11:56.
(type your answer using exponential notation.)

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

Explanation:

Determine the growth model

Using the Bacterial Growth Modeling and Exponential Growth knowledge points

$$
LATEXBLOCK0
$$

Calculate the number of bacteria at 11:56

Using the Bacterial Growth Modeling and Exponential Growth knowledge points

$$
LATEXBLOCK1
$$

Determine the fraction of the bottle filled at 11:56

Using the Bacterial Growth Modeling and Exponential Growth knowledge points

$$
LATEXBLOCK2
$$

Answer:

There will be <blank>\(2^{56}\)</blank> bacteria in the bottle at 11:56.
The bottle will be <blank>\(\frac{1}{16}\)</blank> full at that time.