Chapter 8.5, Problem 5CYU

To determine

To find: The air pressure at the summit in pascals for each mountain listed in the given table.

Answer to Problem 5CYU

The air pressure at the Everest, Trisuli, Bonete, McKinley and Canada are $26,855$ , $34,963$ , $36,028$ , $39,846$ and $41,261$ respectively.

Explanation of Solution

Given:

The logarithmic equation is $a=15,500\left(5-{\log }_{10}P\right)$ .

Calculation:

Solve the given logarithmic equation for $P$ .

  $\begin{array}{c}a=15,500\left(5-{\log }_{10}P\right)\\ a=77500-15500{\log }_{10}P\\ 15500{\log }_{10}P=77500-a\\ {\log }_{10}P=\frac{77500-a}{15500}\end{array}$

Simplify further.

  $P={10}^{\frac{77500-a}{15500}}$

Substitute $a=8850$ to find the air pressure at the Everest.

  $\begin{array}{c}P={10}^{\frac{77500-8850}{15500}}\\ \approx 26,855\end{array}$

Substitute $a=7074$ to find the air pressure at the Trisuli.

  $\begin{array}{c}P={10}^{\frac{77500-7074}{15500}}\\ \approx 34,963\end{array}$

Substitute $a=6872$ to find the air pressure at the Bonete.

  $\begin{array}{c}P={10}^{\frac{77500-6872}{15500}}\\ \approx 36,028\end{array}$

Substitute $a=6194$ to find the air pressure at the McKinley.

  $\begin{array}{c}P={10}^{\frac{77500-6194}{15500}}\\ \approx 39,846\end{array}$

Substitute $a=5959$ to find the air pressure at the Canada.

  $\begin{array}{c}P={10}^{\frac{77500-5959}{15500}}\\ \approx 41,261\end{array}$

Therefore, the air pressure at the Everest, Trisuli, Bonete, McKinley and Canada are $26,855$ , $34,963$ , $36,028$ , $39,846$ and $41,261$ respectively.