Directions: Work out these problems on scratch paper rst, then write your nal answers by hand on these pages. Show all work, and answer each question that is asked. All graphs should be drawn accurately on this sheet and be fully labeled. Upload to 13215. 1. A certain lake is stocked with 3000 sh. The population, P, is growing according to a logistic curve: 9,000 13 = 1 + zero-2' Print where t is measured in months since the lake was initially stocked. a. Graph this function with appropriate scales, showing all intercepts and asymptotes within the domain. b. After how many months will the sh population be 7000? Solve algebraically and round to the nearest 0.1 months. Print 0. Is there a maximum possible sh population that the lake can sustain, according to this model? If so, what is the maximum population? How do you know? (Hint: look at the long-term behavior of the graph.)