1. A certain lake is stocked with 3000 fish. The population, P, is growing according to a logistic curve: 9,000 I+2e-0.21 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 fish population be 7000? Solve algebraically and round to the nearest 0.1 months. c. Is there a maximum possible fish population that the lake can sustain, according to this model? If so, what is the maximum population? How do you know?