SOLUTION: I am stumped on the following question: the current population of the US is 317,000,000 and the current national debt is $17,000,000,000. Based on these figures, use algebraic e

Question 964344: I am stumped on the following question:
the current population of the US is 317,000,000 and the current national debt is $17,000,000,000. Based on these figures, use algebraic equations to calculate the approximate amount of debt per citizen. Assume the population growth is a linear function that grows at a steady unchanging rate of 0.9% per year and the debt growth is a lower function that grows at a steady unchanging rate of 13% per year. Use the population and debt figure from the previous equation to solve. Find the linear equation for population in slope intercept form. Find the linear equation for debt in slope intercept form.
This is what I came up with, however, I am having problems with graphing and the conversion. My teacher told me the answer I submitted was wrong. ANy help would be appreciated
My solution:
Approximate amount of debt per citizen =
Debt = $17,000,000,000
Population = 317,000,000
Equation: $17,000,000,000/317,000,000
Therefore, the approximate debt per citizen will be $53,627.76
2. Slope Intercept Equation for population:
0.9(#of years) + population = growth which will be 9/10x+317=y
Slope Intercept Equation for Debt
0.13(# of years) + debt = growth = 13/100x +17 = y
3. Population in 30 years = 344 million
National Debt in 30 years = 20.9 trillion
Debt per citizen in 30 years = $60,753.81
4. F(30)=0.13x +17/g(30)=0.9x +317
Debt over population in 20 years = 19.6/35
Debt per citizen in 20 years = $58,507.46
X y
0 53,627.76
10 53,696.76
20 53,765.76
The graph is a linear function because there is not sufficient data accumulated to produce a non linear function.
5. 5 years = 17(1*0.08/1)^(1)5 = 25 trillion
10 years = 17(1*0.08/1)^(1)10=36.7 trillion
20 years = 17(1*0.08/1)^(1)20=78.25 trillion
6. 17(1*0.08/1)^y=19.72
Therefore, during the first year, the debt will accrue 1.36 trillion dollars of interest
17(1*0.08/1)^y=19.72
As a result, it will take about 1.93 years to double the expense of the first year

Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
This part of the description is no good because it is inconsistent:

Assume the population growth is a linear function that grows at a steady unchanging rate of 0.9% per year and the debt growth is a lower function that grows at a steady unchanging rate of 13% per year.
A percentage of a variable versus time is exponential, NOT linear.

Otherwise, the first question, the debt per citizen is the ratio dollars per person.

The only way to make sense of the description is to use the given percentages based on the given VALUES for debt and for the population, so these percents will then be made as FIXED constants. This is because you are expecting linear relationships instead of exponential ones.

Population growth would be persons per year, and debt growth would need to be dollars per year.
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