Question

A certain culture of the bacterium Rhodobacter sphaeroides initially has 20 bacteria and is observed to double every 6 hours.

(a) Find an exponential model n(t)=n₀2ᵗ/ᵃ for the number of bacteria in the culture after t hours.
n(t)=

Answer 1

The exponential model for the growth of the bacterium Rhodobacter sphaeroides starting with 20 bacteria and doubling every 6 hours is n(t) = 20 ²⁴/₆.

Step-by-step explanation:

The student is asked to find an exponential model n(t)=n₀²2ᵀ/ₐ for the number of bacteria in the culture after t hours, where n₀ is the initial number of bacteria, t is time in hours, and a is the number of hours it takes for the population to double.

To find the model, we take into account that initially, there are 20 bacteria and the bacteria double every 6 hours. Therefore, the model for the number of bacteria after t hours will be:

n(t) = 20 ²t/6

Exponential growth in bacteria is an important concept that reflects how the growth rate of a population increases over time, resulting in a J-shaped growth curve when plotted. This understanding is crucial for predicting the population size of bacteria under ideal conditions.

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