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 bacteria in the bottle at 11:56.
(type your answer using exponential notation.)

Explanation:

Determine the growth model

Using the Bacterial Growth Modeling and Exponential Growth knowledge points

$$ N(t) = N_0 \cdot 2^t $$

where \(N_0 = 1\) at 11:00 am (\(t = 0\)), and \(t\) is the number of minutes past 11:00 am.

Calculate the number of bacteria at 11:56

Using the Bacterial Growth Modeling and Exponential Growth knowledge points

$$
LATEXBLOCK0
$$

Calculate the fraction of the bottle filled

Using the Bacterial Growth Modeling and Exponential Growth knowledge points

$$
LATEXBLOCK1
$$

Answer:

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 <blank>\(2^{56}\)</blank> bacteria in the bottle at 11:56.
(Type your answer using exponential notation.)