Chapter 3.7, Problem 82E

 Cell population The population of a culture of cells after t days is approximated by the function

  $P\left(t\right)=\frac{1600}{1+7e^{-0.02t}},\text{for }t\ge 0$

1. a. Graph the population function.
2. b. What is the average growth rate during the first 10 days?
3. c. Looking at the graph, when does the growth rate appear to be a maximum?
4. d. Differentiate the population function to determine the growth rate function P′(t).
5. e. Graph the growth rate When is it a maximum and what is the population at the time that the growth rate is a maximum?