AutoSave Differential - Saved to this PC Sign in ox File Home Insert Review View Help O Search Share Comments Bo Link Header HA HH Design Layout References Mailings Pictures Icons ch Chart Online Pictures 3D Models - Screenshot Shapes 2 SmartArt Cover Page Blank Page Page Break Get Add-ins My Add-ins - Wikipedia TT Equation - Symbol Table Online Bookmark Cross-reference Comment Footer Page Number Text Box - A- As a Video Pages Tables Illustrations Add-ins Media Links Comments Header & Footer Text Symbols Q. Suppose the population of fish in a lake grows 10% per year, and in year t=0, the population is 500 fish. At time t=1 year, the lake is instantaneously stocked with 2000 fish. (a) Write an IVP involving the Delta function that models the population of fish in the lake, and solve it. Then write your solution as a piecewise defined function (instead of something involving unit step functions). Hint: Without the Delta function, the ODE would just describe simple exponential growth b) Now suppose that after 6 years, we decide the population is too large, and allow people to fish in the lake. We give out fishing licenses to allow a constant H fish to be removed from the lake each year, so that our ODE from part (a) now includes the term -HU(t-6)-HU(t-6). Solve this new IVP, and write your solution as a piecewise defined function (instead of something involving unit step funcitons c) For your solution to part (b), find the (approximate) value of H that would lead to a constant (i.e. sustainable) population of fish in the lake, and find the size of this constant equilibrium population Page 1 of 1 192 words DE 100% Type here to search O 11:08 PM 6/9/2020 99+ la (1) AutoSave Differential - Saved to this PC Sign in ox File Home Insert Review View Help O Search Share Comments Bo Link Header HA HH Design Layout References Mailings Pictures Icons ch Chart Online Pictures 3D Models - Screenshot Shapes 2 SmartArt Cover Page Blank Page Page Break Get Add-ins My Add-ins - Wikipedia TT Equation - Symbol Table Online Bookmark Cross-reference Comment Footer Page Number Text Box - A- As a Video Pages Tables Illustrations Add-ins Media Links Comments Header & Footer Text Symbols Q. Suppose the population of fish in a lake grows 10% per year, and in year t=0, the population is 500 fish. At time t=1 year, the lake is instantaneously stocked with 2000 fish. (a) Write an IVP involving the Delta function that models the population of fish in the lake, and solve it. Then write your solution as a piecewise defined function (instead of something involving unit step functions). Hint: Without the Delta function, the ODE would just describe simple exponential growth b) Now suppose that after 6 years, we decide the population is too large, and allow people to fish in the lake. We give out fishing licenses to allow a constant H fish to be removed from the lake each year, so that our ODE from part (a) now includes the term -HU(t-6)-HU(t-6). Solve this new IVP, and write your solution as a piecewise defined function (instead of something involving unit step funcitons c) For your solution to part (b), find the (approximate) value of H that would lead to a constant (i.e. sustainable) population of fish in the lake, and find the size of this constant equilibrium population Page 1 of 1 192 words DE 100% Type here to search O 11:08 PM 6/9/2020 99+ la (1)
