Question

the formula (p = 14.7e^{-0.21x}) gives the average atmospheric pressure (p), in pounds per square - inch, at an altitude (x), in miles above sea level. find the elevation of a jet if the atmospheric pressure outside the jet is 7.6 lb/in². the elevation of the jet is approximately (square) miles. (do not round until the final answer. then round to the nearest tenth as needed.)

Explanation:

Step1: Set up the equation

We are given the formula $P = 14.7e^{- 0.21x}$, and $P = 7.6$. So we set up the equation $7.6=14.7e^{-0.21x}$.

Step2: Isolate the exponential term

Divide both sides of the equation by 14.7: $\frac{7.6}{14.7}=e^{-0.21x}$, which simplifies to approximately $0.517 = e^{-0.21x}$.

Step3: Take the natural - logarithm of both sides

$\ln(0.517)=\ln(e^{-0.21x})$. Since $\ln(e^{a}) = a$, we have $\ln(0.517)=-0.21x$.

Step4: Solve for x

We know that $\ln(0.517)\approx - 0.659$. Then $x=\frac{-0.659}{-0.21}\approx3.138$.

Answer:

$3.1$