The number of country A forces in country B decreased to approximately 34,000 in 2014 from a high of about 100,000 in 2008. The amount of country A funding for country B security forces also decreased during this period. The function f (x) = -1.330x + 5.149x +5.517 can be used to estimate the amount of country A funding for country B security forces, in billions of dollars, x years after January 2007. In what year was the amount of country A funding for country B security forces about $ 10.5 billion?

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MRROYALGO MRROYALGO · Answer 1

Answer:

2009

Step-by-step explanation:

The question can be interpreted as:

[tex]f(x) = -1.330x^2 + 5.149x + 5.517[/tex]

Required

Determine x when f(x) = 10.5

Substitute 10.5 for f(x) in [tex]f(x) = -1.330x^2 + 5.149x + 5.517[/tex]

[tex]10.5 = -1.330x^2 + 5.149x + 5.517[/tex]

Collect Like Terms

[tex]-1.330x^2 + 5.149x + 5.517-10.5=0[/tex]

[tex]-1.330x^2 + 5.149x -4.983=0[/tex]

Using quadratic formula

[tex]x = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}[/tex]

Where

[tex]a = -1.330[/tex]

[tex]b = 5.149[/tex]

[tex]c = -4.983[/tex]

[tex]x = \frac{-5.149 \± \sqrt{5.149^2 - 4*-1.330*-4.983}}{2*-1.330}[/tex]

[tex]x = \frac{-5.149 \± \sqrt{0.002641}}{-2.660}[/tex]

[tex]x = \frac{-5.149 \± 0.0514}{-2.660}[/tex]

Split:

[tex]x = \frac{-5.149 + 0.0514}{-2.660}\ or\ x = \frac{-5.149 - 0.0514}{-2.660}[/tex]

[tex]x = \frac{-5.0976}{-2.660}\ or\ x = \frac{-5.2004}{-2.660}[/tex]

[tex]x = 1.92\ or\ x = 1.96[/tex]

Both values of x approximates to 2.

So:

[tex]x = 2[/tex]

2 years after 2007 is 2009.

Hence, the funding is about $10.5 billion in 2009