Answer
To find the height of the skyscraper, measure atmospheric pressure at top as well as as at the bottom of the skyscraper, and using the function, find the altitudes ${{a}_{t}}\ \text{and }{{a}_{b}}$.
Work Step by Step
The expression, $P={{P}_{0}}{{e}^{-0.00004a}}$
Here, to find the height of the skyscraper, measure the atmospheric pressure ${{P}_{t}}$ at the top of the skyscraper and then calculate the altitude ${{a}_{t}}$ with the help of the function $P={{P}_{0}}{{e}^{-0.00004a}}$.
Now, measure the atmospheric pressure ${{P}_{b}}$ at the bottom of the skyscraper and then calculate the altitude ${{a}_{b}}$ with the help of the function $P={{P}_{0}}{{e}^{-0.00004a}}$.
Finally, subtract the altitude of the bottom ${{a}_{b}}$ from the altitude of the top ${{a}_{t}}$ of the skyscraper.
So, the height of the skyscraper is ${{a}_{t}}-{{a}_{b}}$.
