QuestionFind the year when the federal debt $y = 1.18x + 1.71$ reaches \ $35.93 trillion, where$ x$ is years after 2000.

Studdy Solution

STEP 1

Assumptions1. The gross federal debt $y$ is in trillions of dollars. The year $x$ is the number of years after20003. The relationship between $y$ and $x$ is given by the equation $y =1.18x +1.71$
4. We are asked to find the year when the federal debt will be $35.93$ trillion

STEP 2

First, we need to find the value of $x$ when $y =35.93$ . We can do this by setting $y$ to $35.93$ in the given equation and solving for $x$ .
$35.93 =1.18x +1.71$

STEP 3

Next, we subtract $1.71$ from both sides of the equation to isolate the term with $x$ .
$35.93 -1.71 =1.18x$

STEP 4

Calculate the left side of the equation.
$34.22 =1.18x$

STEP 5

Now, we divide both sides of the equation by $1.18$ to solve for $x$ .
$x = \frac{34.22}{1.18}$

STEP 6

Calculate the value of $x$ .
$x = \frac{34.22}{1.18} \approx29$

STEP 7

Since $x$ represents the number of years after2000, we add2000 to $x$ to find the actual year.
$Year =2000 + x$

STEP 8

Plug in the value of $x$ to calculate the year.
$Year =2000 +29$

STEP 9

Calculate the year.
$Year =200 +29 =2029$ In the year2029, the federal debt will be $35.93$ trillion.

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QuestionFind the year when the federal debt $y = 1.18x + 1.71$ reaches \ $35.93 trillion, where$ x$ is years after 2000.

Studdy Solution

STEP 1

Assumptions1. The gross federal debt $y$ is in trillions of dollars. The year $x$ is the number of years after20003. The relationship between $y$ and $x$ is given by the equation $y =1.18x +1.71$
4. We are asked to find the year when the federal debt will be $35.93$ trillion

STEP 2

First, we need to find the value of $x$ when $y =35.93$ . We can do this by setting $y$ to $35.93$ in the given equation and solving for $x$ .
$35.93 =1.18x +1.71$

STEP 3

Next, we subtract $1.71$ from both sides of the equation to isolate the term with $x$ .
$35.93 -1.71 =1.18x$

STEP 4

Calculate the left side of the equation.
$34.22 =1.18x$

STEP 5

Now, we divide both sides of the equation by $1.18$ to solve for $x$ .
$x = \frac{34.22}{1.18}$

STEP 6

Calculate the value of $x$ .
$x = \frac{34.22}{1.18} \approx29$

STEP 7

Since $x$ represents the number of years after2000, we add2000 to $x$ to find the actual year.
$Year =2000 + x$

STEP 8

Plug in the value of $x$ to calculate the year.
$Year =2000 +29$

STEP 9

Calculate the year.
$Year =200 +29 =2029$ In the year2029, the federal debt will be $35.93$ trillion.

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QuestionFind the year when the federal debt y=1.18x+1.71y = 1.18x + 1.71y=1.18x+1.71 reaches \35.93trillion,where35.93 trillion, where 35.93trillion,wherex$ is years after 2000.

Studdy Solution

STEP 1

STEP 2

First, we need to find the value of xxx when y=35.93y =35.93y=35.93. We can do this by setting yyy to 35.9335.9335.93 in the given equation and solving for xxx.35.93=1.18x+1.7135.93 =1.18x +1.7135.93=1.18x+1.71

STEP 3

Next, we subtract 1.711.711.71 from both sides of the equation to isolate the term with xxx.35.93−1.71=1.18x35.93 -1.71 =1.18x35.93−1.71=1.18x

STEP 4

Calculate the left side of the equation.34.22=1.18x34.22 =1.18x34.22=1.18x

STEP 5

Now, we divide both sides of the equation by 1.181.181.18 to solve for xxx.x=34.221.18x = \frac{34.22}{1.18}x=1.1834.22​

STEP 6

Calculate the value of xxx.x=34.221.18≈29x = \frac{34.22}{1.18} \approx29x=1.1834.22​≈29

STEP 7

Since xxx represents the number of years after2000, we add2000 to xxx to find the actual year.Year=2000+xYear =2000 + xYear=2000+x

STEP 8

Plug in the value of xxx to calculate the year.Year=2000+29Year =2000 +29Year=2000+29

STEP 9

Calculate the year.Year=200+29=2029Year =200 +29 =2029Year=200+29=2029In the year2029, the federal debt will be 35.9335.9335.93 trillion.

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QuestionFind the year when the federal debt $y = 1.18x + 1.71$ reaches \ $35.93 trillion, where$ x$ is years after 2000.

First, we need to find the value of $x$ when $y =35.93$ . We can do this by setting $y$ to $35.93$ in the given equation and solving for $x$ .
$35.93 =1.18x +1.71$

Next, we subtract $1.71$ from both sides of the equation to isolate the term with $x$ .
$35.93 -1.71 =1.18x$

Calculate the left side of the equation.
$34.22 =1.18x$

Now, we divide both sides of the equation by $1.18$ to solve for $x$ .
$x = \frac{34.22}{1.18}$

Calculate the value of $x$ .
$x = \frac{34.22}{1.18} \approx29$

Since $x$ represents the number of years after2000, we add2000 to $x$ to find the actual year.
$Year =2000 + x$

Plug in the value of $x$ to calculate the year.
$Year =2000 +29$

Calculate the year.
$Year =200 +29 =2029$ In the year2029, the federal debt will be $35.93$ trillion.