High School

Example 7:
An otherwise typical bacterial cell increases from one cell to 256 cells in 10 hours. What is the generation time of this organism?

Example 8:
Escherichia coli has a doubling time of 20 minutes. If there are 5 cells at the beginning of the experiment, how many will there be in 3 hours?

Example 9:
You perform a serial dilution and determine that the original number of cells in your sample was 12,000. How many bacteria will be present in 12 hours if the generation time is 15 minutes (assume unlimited food and a clean environment)?

Example 10:
You determine that a coconut cream pie has 3 million (3 x 10^6) Staph. aureus cells in it. You estimate that the food preparer did not wash his hands and probably inoculated the cream with 500 Staph. aureus. He also forgot to refrigerate it. If the pie was made 6 hours ago, how many generations have occurred? How long is each generation?

Example 11:
Using the generation time from problem 9, how many bacteria would be present after 8 hours at room temperature?

Example 12:
Let's say that flesh-eating Strep. pyogenes divides every 10 minutes at body temperature. You fall down and scrape your knee and get infected with 5 Strep. pyogenes cells. After 4 hours, without medical intervention, how many bacteria will be ravaging your body? Let's say that for every 1 million bacteria, a centimeter of flesh is consumed. After 4 hours, how much tissue would be lost? Are you still alive, and would you want to be?

Answer :

Tissue consumed = 8.39 cm²Assuming that 1 cm² of flesh is consumed per hour, 8.39 cm² of flesh would be lost. It's difficult to say whether you'd be alive or not since it would depend on a variety of factors like the location of the wound, the person's immune system, and so on.

Given,

Number of cells at the beginning = 1

Number of cells after 10 hours = 256

The generation time can be calculated using the formula given below:

G = t/nlog2

Where, G = Generation time. t = Time taken. n = Number of generations.

G = 10/8log2G = 1.25 hours

Given,

Doubling time of E. coli = 20 minutes

Number of cells at the beginning = 5

Number of hours = 3

First, we need to convert the number of hours into minutes.

Number of minutes = 3 × 60 = 180

Number of generations can be calculated using the formula given below:

n = t/g

Where, n = Number of generations. t = Time taken. g = Generation time.

n = 180/20n = 9

The total number of cells can be calculated using the formula given below:

N = 5 × 2⁹N = 2560

Given, Initial number of cells = 12,000

Generation time = 15 minutes

Number of hours = 12

The number of generations can be calculated using the formula given below:

n = t/g

Where, n = Number of generations. t = Time taken. g = Generation time.

Number of minutes = 12 × 60 = 720n = 720/15n = 48

The final number of cells can be calculated using the formula given below:

N = N₀ × 2ⁿ

Where, N = Final number of cells. N₀ = Initial number of cells. n = Number of generations.

N = 12,000 × 2⁴⁸N = 5.74 × 10²³

Given, Number of Staph.

aureus in the pie = 3 × 10⁶

Estimated number of inoculated Staph.

aureus cells = 500

Time elapsed since the pie was made = 6 hours

The number of generations can be calculated using the formula given below:

n = t/g

Where, n = Number of generations. t = Time taken. g = Generation time.

Number of minutes = 6 × 60 = 360n = 360/30n = 12

The final number of cells can be calculated using the formula given below:

N = N₀ × 2ⁿ

Where, N = Final number of cells. N₀ = Initial number of cells. n = Number of generations.

N = 500 × 2¹²N = 2.05 × 10⁸

Given, Generation time = 15 minutes

Number of hours = 8

The number of generations can be calculated using the formula given below:

n = t/g

Where, n = Number of generations. t = Time taken. g = Generation time.

Number of minutes = 8 × 60 = 480n = 480/15n = 32

The final number of cells can be calculated using the formula given below:

N = N₀ × 2ⁿ

Where, N = Final number of cells. N₀ = Initial number of cells. n = Number of generations.

N = 1 × 2³²N = 4,29,49,67,296

Given, Doubling time of Strep.

pyogenes = 10 minutes

Number of cells at the beginning = 5

Number of hours = 4

The number of generations can be calculated using the formula given below:

n = t/g

Where, n = Number of generations. t = Time taken. g = Generation time.

Number of minutes = 4 × 60 = 240n = 240/10n = 24

The final number of cells can be calculated using the formula given below:

N = N₀ × 2ⁿ

Where, N = Final number of cells. N₀ = Initial number of cells. n = Number of generations.

N = 5 × 2²⁴N = 8,388,608

The tissue consumed can be calculated using the formula given below:

Tissue consumed = Number of bacteria × Tissue consumed per bacteria

Tissue consumed = 8,388,608 × (1/1,000,000)

Tissue consumed = 8.39 cm²

Learn more about Generation time from the given link:

https://brainly.com/question/15104570

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Final answer:

The 'generation time' of bacteria is the period needed for a population to double, which varies greatly depending on the species and environment. Bacteria exhibit exponential growth under ideal conditions, but this is theoretical as environmental factors ultimately limit growth. The calculation of bacterial growth rates is crucial for understanding their impact on health and the environment.

Explanation:

Understanding Bacterial Growth and Generation Time

The concept of generation time is central to understanding bacterial growth. In bacteria, generation time refers to the time it takes for a population to double through binary fission. For example, if a bacterial species has a generation time of 30 minutes, a single cell can theoretically give rise to 281,474,976,710,656 cells in 24 hours, since it would undergo 48 doublings (248). It's important to acknowledge that growth rates and generation times can differ significantly among bacterial species and environmental conditions.

Exponential growth is exemplified by bacteria in optimal conditions. Starting with 1,000 bacteria in an environment with unlimited nutrients, the number would double every hour, producing a J-shaped growth curve over time. However, these numbers are theoretical as environmental limitations and other growth factors will impact the actual growth rate. In reality, a one-liter jar holding 1016 bacteria would be surpassed after 24 hours of such growth, emphasizing that in practice, bacterial cultures eventually face limiting factors that slow and halt growth.

In the case of an infection with flesh-eating Streptococcus pyogenes, with a doubling time of 10 minutes, an initial population of 5 cells can increase to approximately 5 x 224 in 4 hours. This demonstrates the severity of bacterial infections and the necessity for timely medical intervention. Calculation of such scenarios helps us understand the potential impact of bacterial growth on health.