Textbook Problem

Biology The population y of a bacterial culture is modeled by the logistic growth function $y=925/\left(1+e^{-0.3t}\right)$, where t is the time in days.

(a) Use a graphing utility to graph the model. Find the number of days it takes for the population to reach 711.

(b) Does the population have a limit as t increases without bound? Explain your answer.

(c) How does the limit change when the model is $y=1000/\left(1+e^{-0.3t}\right)$

? Explain your answer. Draw some conclusions about this type of model.