Create a report summarizing some uses for slope fields. Your typed report should include your solutions to Parts 1 and Parts 2 for completion and at least one paragraph reflecting your overall approach of this project. Your report should also include a detailed solution to this final question: The slope field for a population P is modeled by dP dt Here, P(t) denotes a population size at a given time, t. Write your report in paragraphs, making sure that the reader clearly obtain the answers to questions (a)-(d) presented below in the body of your report. 7.5P-5P. (a) Using a computer math program (Bluffton Slopefield Generator, Desmos, MATLAB, etc), sketch three non-zero solution curves showing different types of behavior for the population P. Provide (describe mathematically) an initial condition that will produce each of the different types of behavior. (b) Is there a stable value of the population? If so, give the value; in either case, explain why or why not. (c) Considering the shape of solutions for the population, give any intervals for which the following are true: P is increasing when P is in. P is decreasing when P is in. Think about what these conditions mean for the population, and be surethat you are able to ex- plain that. In the long-run (as to), what is the most likely outcome for the population? P (d) Sketch a graph of dP/dt against P. Use your graph to answer the following questions. When is dP/dt positive? When is dP/dt negative? When is dP/dt zero? When is dP/dt at a maximum? Be sure that you can see how the shape of your graph of dP/dt explains the shape of solution curves to the differential equation.