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 