Chapter 4.4, Problem 20PFA

To determine

To find: The height of the building at 6 months.

Answer to Problem 20PFA

The height of the building at 6 months is B. 171 ft.

Explanation of Solution

Given information:

The table shows the height of a skyscraper during its construction. Also, use 9 and 18 months to write the equation for the line of fit.

Month ( x )	0	9	12	18	20
Height in feet ( y )	26	252	345	495	553

Calculation:

From the table, consider the points (9,252) and (18,495) to find the equation of the line of fit using two-point form.

So, the equation of the line of it will be given by,

  $\frac{y-y_1}{y_2-y_1}=\frac{x-x_1}{x_2-x_1}$

Now, $x_1=9,y_1=252,x_2=18,y_2=495$

Therefore, the equation of the line of fit will be,

  $\begin{array}{l}\frac{y-252}{495-252}=\frac{x-9}{18-9}\\ \therefore \frac{y-252}{243}=\frac{x-9}{9}\\ \therefore \frac{y-252}{27}=x-9\\ \therefore y-252=27x-243\\ \therefore y=27x+252-243\end{array}$

  $\therefore y=27x+9$…(1)

Now, at 6 months, $x=6$ , we need to find the corresponding value of y . So, plugging $x=6$ in equation (1).

  $\begin{array}{l}y=27(6)+9\\ \therefore y=171\end{array}$

Conclusion:

Therefore, the height of the skyscraper will be 171 feet at 6 months.