Chapter 4, Problem 87RE

(a)

To determine

The atmospheric pressure at an altitude of $2$ kilometers, where

$f(x)=1035e^{-0.12x}$ is the atmospheric pressure in ${\text{g/cm}}^{\text{2}}$ at altitude $x$ kilometers. The graphs of $f(x)$ and $f\text{'}(x)$ are as follows:

(b)

To determine

The altitude at which the atmospheric pressure is $200{\text{g/cm}}^{\text{2}}$, where $f(x)=1035e^{-0.12x}$ is the atmospheric pressure in ${\text{g/cm}}^{\text{2}}$ at altitude $x$ kilometers. The graphs of $f(x)$ and $f\text{'}(x)$ are as follows:

(c)

To determine

The rate at which the atmospheric pressure is changing at an altitude of $8$ kilometers, where $f(x)=1035e^{-0.12x}$ is the atmospheric pressure in ${\text{g/cm}}^{\text{2}}$ at altitude $x$ kilometers. The graphs of $f(x)$ and $f\text{'}(x)$ are as follows:

(d)

To determine

The altitude at which the atmospheric pressure is failing is at the rate of $100{\text{g/cm}}^{\text{2}}$ per kilometer, where $f(x)=1035e^{-0.12x}$ is the atmospheric pressure in ${\text{g/cm}}^{\text{2}}$ at altitude $x$ kilometers.