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Year Net Profit D 2000 9,381 D O aut a₁ + a₂ + a,= 9,381 a+2a+ 2a + 2a,= 10,394 ao+ 4a₁+ 4a₂+ 4a, 11,330 a+ 6a₁ + 6a₂+ 6a, = 12,489 2001 10,023 at a₁ + a₂+ a,= 9,381 10,394 a+ 3a₁ + 3a₂+ 3a, a+ Sa,+ Sa₂+ Sa, 11,330 a+ 7a,+ 7a₂+ 7a, = 12,489 a₁ + a₁ + a₂+ a+2a₁+ 4a₂+ Sa, 49,381 10,394 a+ 4a₁ + 16a₂+ 64a, 11,330 a+ 6a₁ + 36a₂+ 216a,= 12,489 as + a₂ + a₂ + Gy do + 3a1 +9a2 + 27as ao +501 + 25a + 125a, ag+7a1 +49a2 + 343a, A cubic model p(x)=a+a,x+a,x²+a,' that matches the data for the years 2001, 2003, 2005, and 2007 is to be determined where x represents the number of years since 2000. Set up a system of equations to solve for the coefficients a, a, a, and a. 10,023 10,486 12, 355 14, 400 2002 10,394 ao + a₁ + a₂ + a, = 10,023 a₂ + a₁ + a₂ + a, = 10,486 ao + a₁ + a₂ + a, = 12,355 ao + a₁ + a₂ + a₂ = 14,400 2003 10,486 2004 11,330 2005 12,355 2006 12,489 2007 14,400

Year Net Profit D 2000 9,381 D O aut a₁ + a₂ + a,= 9,381 a+2a+ 2a + 2a,= 10,394 ao+ 4a₁+ 4a₂+ 4a, 11,330 a+ 6a₁ + 6a₂+ 6a, = 12,489 2001 10,023 at a₁ + a₂+ a,= 9,381 10,394 a+ 3a₁ + 3a₂+ 3a, a+ Sa,+ Sa₂+ Sa, 11,330 a+ 7a,+ 7a₂+ 7a, = 12,489 a₁ + a₁ + a₂+ a+2a₁+ 4a₂+ Sa, 49,381 10,394 a+ 4a₁ + 16a₂+ 64a, 11,330 a+ 6a₁ + 36a₂+ 216a,= 12,489 as + a₂ + a₂ + Gy do + 3a1 +9a2 + 27as ao +501 + 25a + 125a, ag+7a1 +49a2 + 343a, A cubic model p(x)=a+a,x+a,x²+a,' that matches the data for the years 2001, 2003, 2005, and 2007 is to be determined where x represents the number of years since 2000. Set up a system of equations to solve for the coefficients a, a, a, and a. 10,023 10,486 12, 355 14, 400 2002 10,394 ao + a₁ + a₂ + a, = 10,023 a₂ + a₁ + a₂ + a, = 10,486 ao + a₁ + a₂ + a, = 12,355 ao + a₁ + a₂ + a₂ = 14,400 2003 10,486 2004 11,330 2005 12,355 2006 12,489 2007 14,400

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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O O Year Net Profit O 2000 9,381 2001 10,023 au+ a₁ + a₂+ a = 9,381 a+2a + 2a + 2a,= 10,394 11,330 ao+ 4a₁ + 4a₂+ 4a, a+ 6a₂+ 6a₂+ 6a, = 12,489 a₁ + a₁ + a + 2a₁ + ao+ a₁ + a₂+ a = 9,381 ao+ 3a₁ + 3a₂+ 3a,= 10,394 ao+ Sa₂+ Sa₂+ Say 11,330 ao+ 7a₁ + 7a₂+ 7a, = 12,489 A cubic model p(x)= a +a,x+ax²+a,x³ that matches the data for the years 2001, 2003, 2005, and 2007 is to be determined where x represents the number of years since 2000. Set up a system of equations to solve for the coefficients a, a, az and a. a= 9,381 a₂ + 4a₂+ 8a, =10,394 a + 4a₁ + 16a₂+ 64a, =11,330 a + 6a₁ + 36a₂+ 216a, = 12,489 ao + a₁ + a₂ + a3 =10, 023 a +3a1 +9a₂ + 27as = 10,486 ao +5a1 +25a2 + 125a = 12,355 ao +7a1 +49a2 + 343as = 14, 400 2002 10,394 ao + a₁ + a₂ + a = 10,023 a₂ + a₁ + a₂ + a, = 10,486 ao + a₁ + a₂ + a, = 12,355 ao + a₁ + a₂ + a3 = 14,400 2003 10,486 2004 11,330 2005 12,355 2006 12,489 2007 14,400
Transcribed Image Text:O O Year Net Profit O 2000 9,381 2001 10,023 au+ a₁ + a₂+ a = 9,381 a+2a + 2a + 2a,= 10,394 11,330 ao+ 4a₁ + 4a₂+ 4a, a+ 6a₂+ 6a₂+ 6a, = 12,489 a₁ + a₁ + a + 2a₁ + ao+ a₁ + a₂+ a = 9,381 ao+ 3a₁ + 3a₂+ 3a,= 10,394 ao+ Sa₂+ Sa₂+ Say 11,330 ao+ 7a₁ + 7a₂+ 7a, = 12,489 A cubic model p(x)= a +a,x+ax²+a,x³ that matches the data for the years 2001, 2003, 2005, and 2007 is to be determined where x represents the number of years since 2000. Set up a system of equations to solve for the coefficients a, a, az and a. a= 9,381 a₂ + 4a₂+ 8a, =10,394 a + 4a₁ + 16a₂+ 64a, =11,330 a + 6a₁ + 36a₂+ 216a, = 12,489 ao + a₁ + a₂ + a3 =10, 023 a +3a1 +9a₂ + 27as = 10,486 ao +5a1 +25a2 + 125a = 12,355 ao +7a1 +49a2 + 343as = 14, 400 2002 10,394 ao + a₁ + a₂ + a = 10,023 a₂ + a₁ + a₂ + a, = 10,486 ao + a₁ + a₂ + a, = 12,355 ao + a₁ + a₂ + a3 = 14,400 2003 10,486 2004 11,330 2005 12,355 2006 12,489 2007 14,400
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