The total public debt D (in trillions of dollars) in the United States at the beginning of each year from 2000 through 2008 can be approximated by the model D = 0.032t2 + 0.21t + 5.6, 0 ≤ t ≤ 8
where t represents the year, with t = 0 corresponding to 2000.†

Step-by-step explanation:

Given the equation that modeled the total public debt D (in trillions of dollars) in the United States at the beginning of each year from 2000 through 2008 can be approximated by;

D = 0.032t^2 + 0.21t + 5.6, 0 ≤ t ≤ 8

We are to find the total public debt with the time interval;

when t = 0;

D = 0.032(0)^2 + 0.21(0) + 5.6

D = 5.6 trillion dollars

when t = 1;

D = 0.032(1)^2 + 0.21(1) + 5.6

D = 0.032+0.21+5.6

D = 5.842 trillion dollars

when t = 2;

D = 0.032(2)^2 + 0.21(2) + 5.6

D = 0.128+0.42+5.6

D =  6.148 trillion dollars

when t = 3;

D = 0.032(3)^2 + 0.21(3) + 5.6

D = 0.288+0.63+5.6

D = 6.518 trillion dollars

when t = 4;

D = 0.032(4)^2 + 0.21(4) + 5.6

D = 0.512+0.84+5.6

D = 6.952 trillion dollars

when t = 5;

D = 0.032(5)^2 + 0.21(5) + 5.6

D = 0.8+1.05+5.6

D = 7.45 trillion dollars

when t = 6;

D = 0.032(6)^2 + 0.21(6) + 5.6

D = 1.152+1.26+5.6

D = 8.012 trillion dollars

when t = 7;

D = 0.032(7)^2 + 0.21(7) + 5.6

D = 1.568+1.47+5.6

D = 8.638 trillion dollars

when t = 8;

D = 0.032(8)^2 + 0.21(8) + 5.6

D = 0.032(64)+1.68+5.6

D = 2.048+1.68+5.6

D = 9.328 trillion dollars

From the values gotten, we can see that the total public debt reached or surpassed 7 trillion dollars in 2005

To get the public debt in 2017, we can simply substitute t = 17 into the expression D = 0.032t2 + 0.21t + 5.6

D = 0.032(17)^2 + 0.21(17) + 5.6

D = 0.032(289)+3.57+5.6

D = 9.248+3.57+5.6

D(17) = 18.418 trillion dollars

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hope i