SOLUTION: The Houston Astrodome was the first baseball and football stadium to be completely enclosed. It was completed in 1965 at a cost of 45.35 million dollars. Construction costs hav

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: The Houston Astrodome was the first baseball and football stadium to be completely enclosed. It was completed in 1965 at a cost of 45.35 million dollars. Construction costs hav      Log On


   

Question 936310: The Houston Astrodome was the first baseball
and football stadium to be completely
enclosed. It was completed in 1965 at a cost
of 45.35 million dollars. Construction costs
have increased by approximately 6% each year
since 1965.
If this rate were to continue, how much
would it have cost to build the Astrodome in
2012?
Answer by AnlytcPhil(1806) About Me  (Show Source):
You can put this solution on YOUR website!
The Houston Astrodome was the first baseball
and football stadium to be completely
enclosed. It was completed in 1965 at a cost
of 45.35 million dollars. Construction costs
have increased by approximately 6% each year
since 1965.
If this rate were to continue, how much
would it have cost to build the Astrodome in
2012?
Let x = the year
Let y = the cost to build

When x = 1965, y = 45.35 (million dollars)
When x = 1966, y = 45.35 + 0.06(45.35) = 48.071 (million dollars)

We find the equation of the line which passes through the
points (1965,45.35) and (1966,48.071)

We use the slope formula:

m = %28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29
where (x1,y1) = (1965,45.35)
and where (x2,y2) = (1966,48.071)

m = %2848.071-45.35%29%2F%281966-1965%29=2.721

We use the point-slope formula:

y - y1 = m(x - x1)
where (x1,y1) = (1965,45.35)

y - 45.35 = 2.721(x - 1965)

y - 45.35 = 2.721x - 5346.765
       
        y = 2.721x - 5301.415

Sobstitute x = 2012:

        y = 2.721(2012) - 5301.415
          
        y = 173.237 million dollars or $173,237,000

Edwin