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In the 1930's LF. Richardson proposed that an arms race between two countries could be modeled by a system of differential equations One arms race which can be reasonably well descnbed by differential equations is the US-Soviet Union arms race between 1945 and 1960. If z represents the annual Soviet expenditures on armaments (in billions of dollars) and y represents the corresponding US expenditures, it has been suggested[1] that z and y obey the following differential equations dz 0.45z + 10.5, %3D dt dy 8.2z - 0.8y – 142. dt (a) Find the equilibrium point. (Eer Ye) = (b) Use Darryl Nester's direction field applet to plot some solutions to this system You should choose the x-window and the y-window to include the equilibrium point Then, consider the following histonical data. In 1953, the arms budgets (z, y) were (25.6,71.4) Use this initial condition in the applet. You may want to re-adjust the window. What happens to z and y in the long run, starting from this initial condition? (Enter a numerical value, or infinity if the quantity diverges) (c) The actual expenditures for the USSR and US for the five years following 1953 are shown in the table below. year 1954 1955 1956 1957 1958 USSR (2) 23.9 25 5 23 2 23 22.3 US (y) 61.6 58.3 59 4 61.4 61.4

In the 1930's LF. Richardson proposed that an arms race between two countries could be modeled by a system of differential equations One arms race which can be reasonably well descnbed by differential equations is the US-Soviet Union arms race between 1945 and 1960. If z represents the annual Soviet expenditures on armaments (in billions of dollars) and y represents the corresponding US expenditures, it has been suggested[1] that z and y obey the following differential equations dz 0.45z + 10.5, %3D dt dy 8.2z - 0.8y – 142. dt (a) Find the equilibrium point. (Eer Ye) = (b) Use Darryl Nester's direction field applet to plot some solutions to this system You should choose the x-window and the y-window to include the equilibrium point Then, consider the following histonical data. In 1953, the arms budgets (z, y) were (25.6,71.4) Use this initial condition in the applet. You may want to re-adjust the window. What happens to z and y in the long run, starting from this initial condition? (Enter a numerical value, or infinity if the quantity diverges) (c) The actual expenditures for the USSR and US for the five years following 1953 are shown in the table below. year 1954 1955 1956 1957 1958 USSR (2) 23.9 25 5 23 2 23 22.3 US (y) 61.6 58.3 59 4 61.4 61.4

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.7: Applications
Problem 1EQ: In Exercises 1-12, find the solution of the differential equation that satisfies the given boundary...
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In the 1930's L F. Richardson proposed that an arms race between two countries could be modeled by a system of differential equations. One arms race which can be reasonably well described by differential equations is the US-Soviet Union arms race between 1945 and 1960. If z represents the annual Soviet expenditures on armaments (in billions of dollars) and y represents the corresponding US expenditures, it has been suggested[1] that a and y obey the following differential equations dz -0.45z +10.5, dt dy 8.2x – 0.8y – 142. dt (a) Find the equilibrium point. (we, Ya) = (b) Use Darryl Nester's direction field applet to plot some solutions to this system. You should choose the x-window and the y-window to include the equilibrium point Then, consider the following historical data. In 1953, the arms budgets (2, y) were (25.6,71.4). Use this initial condition in the applet. You may want to re-adjust the window. What happens to a and y in the long run, starting from this initial condition? (Enter a numerical value, or infinity if the quantity diverges.) (c) The actual expenditures for the USSR and US for the five years following 1953 are shown in the table below. year 1954 1955 1956 1957 1958 USSR (2) 23.9 25.5 23.2 23 22.3 US (y) 61.6 58.3 59.4 61.4 61.4 Is this evolution of the values for z and y what the model predicts? ? [1] R Taagepera, G. M. Schiffler, R. T. Perkins and D. L. Wagner, S the data are reasonably consistent with the model systems, XX, 1975). the data leave a region the model says they shouldn't the data show a trajectory that isn't at all consistent with the model
Transcribed Image Text:In the 1930's L F. Richardson proposed that an arms race between two countries could be modeled by a system of differential equations. One arms race which can be reasonably well described by differential equations is the US-Soviet Union arms race between 1945 and 1960. If z represents the annual Soviet expenditures on armaments (in billions of dollars) and y represents the corresponding US expenditures, it has been suggested[1] that a and y obey the following differential equations dz -0.45z +10.5, dt dy 8.2x – 0.8y – 142. dt (a) Find the equilibrium point. (we, Ya) = (b) Use Darryl Nester's direction field applet to plot some solutions to this system. You should choose the x-window and the y-window to include the equilibrium point Then, consider the following historical data. In 1953, the arms budgets (2, y) were (25.6,71.4). Use this initial condition in the applet. You may want to re-adjust the window. What happens to a and y in the long run, starting from this initial condition? (Enter a numerical value, or infinity if the quantity diverges.) (c) The actual expenditures for the USSR and US for the five years following 1953 are shown in the table below. year 1954 1955 1956 1957 1958 USSR (2) 23.9 25.5 23.2 23 22.3 US (y) 61.6 58.3 59.4 61.4 61.4 Is this evolution of the values for z and y what the model predicts? ? [1] R Taagepera, G. M. Schiffler, R. T. Perkins and D. L. Wagner, S the data are reasonably consistent with the model systems, XX, 1975). the data leave a region the model says they shouldn't the data show a trajectory that isn't at all consistent with the model
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