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Using data from 2002 and with projections to 2024, total annual expenditures for national health care (in billions of dollars) can be described by E = 4.61x2 + 43.4x + 1620 where x is the number of years past 2000.† If the pattern indicated by the model remains valid, in what year does the model predict these expenditures will reach $15,315 billion?

Respuesta :

Answer:

In 2050, the predicted expenditure will be $15,315 billion.                  

Step-by-step explanation:

We are given the following in the question:

[tex]E(x) = 4.61x^2 + 43.4x + 1620[/tex]

where E(X) is the total annual expenditure in billions of dollar and x is the number of years past 2000.

We have to estimate the year in which predicted expenditure will be $15,315 billion.

Putting values in the question:

[tex]15315 = 4.61x^2 + 43.4x + 1620\\4.61x^2 + 43.4x - 13695 = 0\\\Rightarrow 4.61(x + 59.41431670282)(x - 50) = 0\\\Rightarrow x = 50[/tex]

Thus, after 50 years from 2000, the predicted expenditure will be $15,315 billion.

Thus, in year 2050, the predicted expenditure will be $15,315 billion.

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