SOLUTION: An office building worth $1million when completed in 2005 is being depreciated linearly over 50 years. What was the book value of the building in 2009? What will it be in 2018? (As

Algebra ->  Real-numbers -> SOLUTION: An office building worth $1million when completed in 2005 is being depreciated linearly over 50 years. What was the book value of the building in 2009? What will it be in 2018? (As      Log On


   

Question 785068: An office building worth $1million when completed in 2005 is being depreciated linearly over 50 years. What was the book value of the building in 2009? What will it be in 2018? (Assume the scrap value is $0.)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Right now, it's worth 1 million dollars. So the first ordered pair is (0, 1) where y is in millions.

In 50 years, it will be worth $0. The second ordered pair is (50,0)

Slope:


Now use the slope formula


m = (y2-y1)/(x2-x1)


m = (0-1)/(50-0)


m = -1/50




y = mx + b

y = (-1/50)x + b

1 = (-1/50)(0) + b

1 = 0 + b

1 = b

b = 1

So the equation is y+=+%28-1%2F50%29x+%2B+1 where again, y is the value of the building in millions of dollars and x is the time in years (since 2005)

Now let's answer the questions


What was the book value of the building in 2009?

y+=+%28-1%2F50%29x+%2B+1

y+=+%28-1%2F50%29%284%29+%2B+1

y+=+-4%2F50+%2B+1

y+=+-0.08+%2B+1

y+=+0.92

y is in millions of dollars, so 0.92 million = 920 thousand dollars


What was the book value of the building in 2009? 920 thousand dollars

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What will it be in 2018?


y+=+%28-1%2F50%29x+%2B+1

y+=+%28-1%2F50%29%2813%29+%2B+1

y+=+-13%2F50+%2B+1

y+=+-0.26+%2B+1

y+=+0.74

y is in millions of dollars, so 0.74 million = 740 thousand dollars


What will it be in 2018? 740 thousand dollars