Answer:
The expression for the number of bacteria after t hours is
Step-by-step explanation:
When introduced into a nutrient broth, the culture grows at a rate proportional to its size.
This means that the size of the population, after t hours, is modeled by the following differential equation:
In which R is the growth rate.
The solution of this differential equation is:
In which P(0) is the initial population.
A culture of the bacterium Salmonella enteritidis initially contains 50 cells.
This means that , and so:
After 1.5 hours, the population has increased to 775.
This means that . We use this to find r. So
The expression is:
The expression for the number of bacteria after t hours is