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Sagot :
y - value
x - year
[tex]24000=a\cdot3+b\\ 19000=a\cdot5+b\\\\ 24000=3a+b\\ -19000=-5a-b\\ ---------\\ 5000=-2a\\ a=-2500\\\\ b+3\cdot(-2500)=24000\\ b-7500=24000\\ b=31500\\\\ \boxed{y=-2500x+31500} [/tex]
a)
[tex]f(x)=-2500x+31500\\ f(x+1)=-2500(x+1)+31500\\ f(x+1)=-2500x-2500+31500\\ f(x+1)=-2500x+29000\\\\ f(x)-f(x+1)=-2500x+31500-(-2500x+29000)\\ f(x)-f(x+1)=-2500x+31500+2500x-29000\\ f(x)-f(x+1)=\boxed{2500}[/tex]
b)
[tex]f(0)=-2500\cdot0+31500=\boxed{31500}[/tex]
c)
[tex]f(10)=-2500\cdot10+31500\\ f(10)=-25000+31500\\ f(10)=\boxed{6500}[/tex]
x - year
[tex]24000=a\cdot3+b\\ 19000=a\cdot5+b\\\\ 24000=3a+b\\ -19000=-5a-b\\ ---------\\ 5000=-2a\\ a=-2500\\\\ b+3\cdot(-2500)=24000\\ b-7500=24000\\ b=31500\\\\ \boxed{y=-2500x+31500} [/tex]
a)
[tex]f(x)=-2500x+31500\\ f(x+1)=-2500(x+1)+31500\\ f(x+1)=-2500x-2500+31500\\ f(x+1)=-2500x+29000\\\\ f(x)-f(x+1)=-2500x+31500-(-2500x+29000)\\ f(x)-f(x+1)=-2500x+31500+2500x-29000\\ f(x)-f(x+1)=\boxed{2500}[/tex]
b)
[tex]f(0)=-2500\cdot0+31500=\boxed{31500}[/tex]
c)
[tex]f(10)=-2500\cdot10+31500\\ f(10)=-25000+31500\\ f(10)=\boxed{6500}[/tex]
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