1. Country X and country Y both aspire to be the first to put an astronaut in orbit, spending Sr and Sy respectively on their rocket programs. (a) After observing the spending over the past few years, a statistician estimates that the spending can be expressed in the following dynamical system: dr -3.2r + 3.5y + 4.7 dy 2.4r – 2.8y + 5.2 dt Are the two countries engaged in a space race? (b) What is the spending of the two countries in this scenario? (c) Country X makes a breakthrough which causes country Y to panic and increase its spending. The new dynamical system is: dr = -3.2r + 3.5y + 4.7 dt dy 3.2r - 3.1y + 5.2 dt %3D

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 23EQ: 23. Consider a simple economy with just two industries: farming and manufacturing. Farming consumes...
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Given the dynamical system
de = – -(1)
3. 5y – 3. 2x +4.7 –
dy
2. 4x – 2. 8y + 5. 2 – – –(2)
dt
where a and y indicate the expenditure
of the countries X and Y respectively.
This model is called Richardson's arms
race model.
dx
dt
my – ax + p –--(3)
dy
dt
= nx – by + q – – -(4)
Ston
Transcribed Image Text:Given the dynamical system de = – -(1) 3. 5y – 3. 2x +4.7 – dy 2. 4x – 2. 8y + 5. 2 – – –(2) dt where a and y indicate the expenditure of the countries X and Y respectively. This model is called Richardson's arms race model. dx dt my – ax + p –--(3) dy dt = nx – by + q – – -(4) Ston
1. Country X and country Y both aspire to be the first to put an astronaut in orbit,
spending Sr and Sy respectively on their rocket programs.
(a) After observing the spending over the past few years, a statistician estimates
that the spending can be expressed in the following dynamical system:
dr
-3.2r + 3.5y + 4.7
dy
2.4x – 2.8y + 5.2
%3D
dt
Are the two countries engaged in a space race?
(b) What is the spending of the two countries in this scenario?
(c) Country X makes a breakthrough which causes country Y to panic and increase
its spending. The new dynamical system is:
dr
= -3.2r + 3.5y + 4.7
dt
dy
3.2r – 3.1y + 5.2
dt
Are the two countries now engaged in a space race?
Transcribed Image Text:1. Country X and country Y both aspire to be the first to put an astronaut in orbit, spending Sr and Sy respectively on their rocket programs. (a) After observing the spending over the past few years, a statistician estimates that the spending can be expressed in the following dynamical system: dr -3.2r + 3.5y + 4.7 dy 2.4x – 2.8y + 5.2 %3D dt Are the two countries engaged in a space race? (b) What is the spending of the two countries in this scenario? (c) Country X makes a breakthrough which causes country Y to panic and increase its spending. The new dynamical system is: dr = -3.2r + 3.5y + 4.7 dt dy 3.2r – 3.1y + 5.2 dt Are the two countries now engaged in a space race?
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