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 proportional to the GNP.

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

b. Solve the system in part (a), assuming the GNP is M₀ and the national debt is N₀ at year 0.

c. Does the national debt eventually outstrip the GNP? Consider the ratio of the national debt to the GNP.