In many lakes with no harvesting, we can use the logistic growth differential equation to model a fish population. Suppose L represents the total number of Lake Sturgeon in our lake, it is currently estimated the lake contains approximately 20,000 Lake Sturgeons, and the lake contains 100 cubic miles of water (similar to estimated totals in Lake Erie) Discuss why it is reasonable to use the logistic growth mathematical model to model the Lake Sturgeon population. Assuming logistic growth, what is the initial value problem (IVP) for the situation described? (Use r = 0.07/yr in your IVP) 2. Use Matlab and Euler's method to create a graphical solution of your IVP in (1) Use time steps of a half-year for 100 years (You may simply modify Logistic.m) . (a) Approximately how many years will it take for the population to attain 60% of the carrying capacity? (b) Suppose the population of Lake Sturgeon in the lake is extremely depleted (which it was in most of the North American lakes) and the entire lake contained only 1000 Lake Sturgeon. Run your logistic m-file again using this new initial condition. Now how long will it take for the population to reach 60% of the carrying capacity? (c) Given that serious conservation efforts for Lake Sturgeons started in North America approximately 45 years ago, are the plots in (a) and (b) consistent? Discuss.