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
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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.
