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the polynomial -3 x 2 +400 X represents the budget surplus of the town of alphaville for the year 2010. Alphaville surplus in 2011 can be modeled by -15 x 2 + 200 x. If x represents the yearly tax revenue in thousands, enter a polynomial for how much alphaville budget surplus increase from 2010 to 2011. If alphaville took in $450,000 in tax revenue in 2011, what was the budget surplus this year?

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ukshedrack

Answer:

Question 1: Budget Surplus Increase = [tex]-12x^{2} -200x[/tex]

Question 2: Budget surplus in 2011 = $[tex]3.04*10^{12}[/tex]

Step-by-step explanation:

Question 1

Budget surplus in 2010 = [tex]-3x^{2} + 400x[/tex]

Budget surplus in 2011 = [tex]-15x^{2} + 200x[/tex]

Increase in buget surplus = Budget surplus in 2011 - Budget surplus in 2010

[tex]-15x^{2} + 200x - (-3x^{2} + 400x)\\\\= -15x^{2} + 200x + 3x^{2} - 400x\\\\= -12x^{2} -200x[/tex]

Question 2

2011 yearly tax revenue, x = $450,000

Budget surplus in 2011 =

[tex]-15x^{2} + 200x = -15(450000)^{2} + 200(450000)\\\\= -15(2.025*10^{11}) + 9*10^{7}\\ \\= (-15*2.025*10000*10^{7}) + (9*10^{7})\\ \\= -303750*10^{7} + 9*10^{7} = (-303750+9)*10^{7}\\ \\= -303741*10^{7} = -3.03741*10^{5}*10^{7}\\\\= -3.03741*10^{12}[/tex]

Budget surplus in 2011 ≅ $[tex]-3.04*10^{12}[/tex]

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