Respuesta :
Answer:
[tex]V=-130000x+1080000[/tex]
Explanation:
Linear Dependence
Some variables are known or assumed to have linear dependence which means the graph of the ordered pairs (x,V) is a straight line.
If we know two points of the line, we can come up with the exact equation and therefore make predictions for other values of x
The linear depreciation gives us these points (2,820000) and (5,430000)
The general equation of the line is
[tex]V=mx+b[/tex]
Where V is the machine value and x is the  number of years after purchase. We need to find the values of m and b.
Replacing the first point
[tex]820000=m(2)+b[/tex]
[tex]2m+b=820000[/tex]
Replacing the second point
[tex]5m+b=430000[/tex]
Subtracting them Â
[tex]-3m=390000[/tex]
[tex]m=-130000[/tex]
Replacing in any of the equations, say, the first one
[tex]2(-130000)+b=820000[/tex]
Solving for b
[tex]b=820000+260000[/tex]
[tex]b=1080000[/tex]
The formula for the machine value V is Â
[tex]\boxed{V=-130000x+1080000}[/tex]
Formula for the machine value V in x year is v = -130000(x) + 1,080,000
Liner depreciation based problem:
What information do we have?
Cost of machine after 2 year = $820,000
Cost of machine after 5 year = $430,000
Liner depreciation equation
v = mx + b
After 2 year
820,000 = m(2) + b
820,000 = 2m + b ......... Â Eq1
After 5 year
430,000 = m(5) + b
430,000 = 5m + b ......... Â Eq2
Eq2 - Eq1
3m = -390,000
m = -130,000
From Eq
430,000 = 5m + b
430,000 = 5(-130,000) + b
b = 1,080,000
Liner equation of tha cost.
Amount of machine = mx + b
Amount of machine = -130000(x) + 1,080,000
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