ECONOMICS: National Debt The national debt (the amount of money that the federal gover...

ECONOMICS: National Debt The national debt (the amount of money that the federal government has borrowed from and therefore owes to the public) is approximately billion dollars, where x is the number of years since 2012. The population of the United States is approximately P(x) = 2.3x + 314 million.

a. Enter these functions into your calculator as y₁ and y₂, respectively, and define y3 to be y₁ ÷ y₂, the national debt divided by the population, so that y₃ is the per capita national debt, in thousands of dollars (since it is billions divided by millions). Evaluate y₃ at 8 and at 13 to find the per capita national debt in the years 2020 and 2025. This is the amount that the government would owe each of its citizens if the debt were divided equally among them.

b. Use the numerical derivative operation NDERIV to find the derivative of y₃ at 8 and at 13 and interpret your answers.