A pastry chef accidentally inoculated a cream pie with six S. aureus cells. If S. aureus has a generation time of 60 minutes, how many cells would be in the cream pie after 7 hours?

Verified step by step guidance

1. Identify the initial number of cells, which is 6 S. aureus cells.
2. Determine the generation time, which is 60 minutes per generation.
3. Calculate the total time in minutes for 7 hours: 7 hours * 60 minutes/hour.
4. Determine the number of generations by dividing the total time by the generation time.
5. Use the formula for exponential growth: Final number of cells = Initial number of cells * 2^(number of generations).

Key Concepts

Bacterial Growth and Generation Time

Bacterial growth refers to the increase in the number of bacterial cells over time. The generation time is the time it takes for a bacterial population to double in number. For S. aureus, the generation time is 60 minutes, meaning that every hour, the number of cells will double, which is crucial for calculating the final cell count after a specific duration.

Exponential Growth Model

Bacteria typically grow in an exponential manner, where the population size increases rapidly as each generation doubles the previous count. This model can be represented mathematically, where the number of cells after a certain time can be calculated using the formula N = N0 * 2^(t/g), where N0 is the initial number of cells, t is the total time, and g is the generation time.

Time Conversion in Calculations

When performing calculations involving time, it is essential to ensure that all time units are consistent. In this case, the total time of 7 hours must be converted into minutes (420 minutes) to match the generation time of S. aureus, which is given in minutes. This conversion is necessary for accurate calculations of bacterial growth over the specified period.