The number of yeast cells in a laboratory culture increases rapidly initially, but levels off eventually toward the maximum population the culture can sustain. The number of cells, (henceforth known as the Population), is modeled by the function: n = f(t) = a/(1+be(-0.7t) ) Where t is time measured in hours. At time t = 0, the population is 20 cells and is increasing at a rate of 12 cells/hour.
a) What does dn/dt represent and what are its units? Explain your conclusion.
b) At any value of t > 0, what would you expect the sign of dn/dt to be? Explain your conclusion.
C) Compute f' (t). Is this derivative the same as dn/dt and does it verify your conclusion to part b? Are there any assumption that need to be made about the values of a and b?
d) Suppose that f(0)=20 cells and the population is increasing at a rate of 12 cells/hour at that point. Find the values of a and b.
e) According to this model, what happens to the yeast population in the long r.