Question

The atmospheric pressure P in pounds per square inch (psi) is given by
P = 14.7 e−0.21 awhere a is the altitude above sea level (in miles). If a city has an atmospheric pressure of 13.11 psi, what is its altitude? (Recall that 1 mi = 5,280 ft. Round your answer to the nearest foot.)

Answer 1

Answer on Question #48883 – Math – Algebra

The atmospheric pressure $P$ in pounds per square inch (psi) is given by

$$P = 14.7 \, e^{\left(-0.21 \, a\right)}$$

, where $a$ is the altitude above sea level (in miles). If a city has an atmospheric pressure of 13.11 psi, what is its altitude? (Recall that $1 \, \text{mi} = 5,280$ ft. Round your answer to the nearest foot.)

Solution.

$$\begin{array}{l} P = 14.7 e^{-0.21a} \rightarrow \ln P = \ln 14.7 - 0.21a \rightarrow \\ \rightarrow a = \frac{\ln 14.7 - \ln P}{0.21} = \frac{\ln 14.7 - \ln 13.11}{0.21} = 0.5451 \, \text{miles}. \\ a = 0.5451 * 5280 = 2878 \, \text{ft}. \end{array}$$

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