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The gross national product (GNP) represents the sum of consumption purchases of goods and services, government...

The gross national product (GNP) represents the sum of consumption purchases of goods and services, government purchases of goods and services, and gross private investment (which is the increase in inventories plus buildings constructed and equipment acquired).

Assume that the GNP is increasing at the rate of 3% per year, and that the national debt is increasing at a rate k = 6% proportional to the GNP.

a) Construct a system of two ordinary differential equations modeling the GNP and national debt.

b)

Solve the system you formulated, assuming the GNP is M0 = 1 and the national debt is N0 = 0.5 at year 0.

What's the value of GNP at year 10?

c) What is the value of the national debt at year 10?

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