(Solved): Objectives: Mathematical Language, Modeling (Mathematization), Modeling (Interpre- tation), Reading ...

Objectives: Mathematical Language, Modeling (Mathematization), Modeling (Interpre-
tation), Reading Mathematics

2. Learning Objectives: Mathematical Language, Modeling (Mathematization), Modeling (Interpretation), Reading Mathematics Suppose that \( N(t) \) represents the number of Wood Bison in population \( t \) years after the population is reintroduced into Southwestern Alaska. We will assume the population is expected to grow according to a logistic growth model. If we assume that the carrying capacity is 500 , then we can arrive at the following differential equation: \[ \frac{d N}{d t}=\frac{r}{500} N(500-N) \] where \( r \) is a constant that denotes the intrinsic growth rate. You can think of this as the growth rate the population would experience with access to unlimited resources and unlimited room to grow. (a) Solve this differential equation. As part of your solution, be sure to provide some explanation of the solution process. Review the in-class activity on the Logistic equation (Wed Sept 14th). Your solution will depend on the parameter \( r \) (b) Assume initially that 100 bison were released into the wild. Use this data to find a particular solution. The model should still include \( r \) as a parameter at this point. (c) Suppose that biologists estimate the intrinsic growth rate to be \( r=0.25 / \mathrm{yr} \). Use Desmos or another graphical tool to plot your solution \( N(t) \) and estimate the time it will take for the population to exceed 450 bison. Make sure to include either a sketch or screenshot of \( N(t) \) as part of your solution. (d) Visit the Alaska Wildlife Conservation Center website describing the reintroduction of wood bison to Southwestern Alaska here: https://www. alaskawildlife.org/wood-bison-restoration/ Provide a 1-2 sentence summary of this project.