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?
<pre>
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 = {{{(y[2]-y[1])/(x[2]-x[1])}}}
where (x<sub>1</sub>,y<sub>1</sub>) = (1965,45.35)
and where (x<sub>2</sub>,y<sub>2</sub>) = (1966,48.071)

m = {{{(48.071-45.35)/(1966-1965)=2.721}}}

We use the point-slope formula:

y - y<sub>1</sub> = m(x - x<sub>1</sub>)
where (x<sub>1</sub>,y<sub>1</sub>) = (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</pre>