💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

The rate of change of atmospheric pressure $P$ with respectto altitude $h$ is proportional to $P$ , provided that the temperature is constant. At $15^{\circ} \mathrm{C}$ the pressure is 101.3 $\mathrm{kPa}$ at sealevel and 87.14 $\mathrm{kPa}$ at $h=1000 \mathrm{m} .$

a) $$64.5 \mathrm{kPa}$$b) $$39.9 \mathrm{kPa}$$

Calculus 1 / AB

Chapter 3

INVERSE FUNCTIONS

Section 4

Exponential Growth and Decay

Derivatives

Differentiation

Applications of the Derivative

Oregon State University

University of Nottingham

Idaho State University

Boston College

Lectures

03:09

In mathematics, precalculu…

31:55

In mathematics, a function…

04:17

The rate of change of atmo…

06:50

Atmospheric pressure The e…

04:00

The atmospheric pressure $…

02:13

Atmospheric Pressure Atmos…

01:00

Physics At a constant temp…

03:18

The atmospheric pressure a…

02:21

Atmospheric Pressure $\Lef…

02:20

Atmospheric pressure $P$ (…

00:53

Air pressure, $P$, decreas…

01:46

The altimeter in an airpla…

03:43

Atmospheric pressure The p…

05:37

04:32

01:28

02:59

Modeling Data The atmosphe…

01:36

Approximate the change in …

01:18

02:14

02:31

When air expands adiabatic…

01:32

Hey, guys, welcome back This problem. You know, the pressure changed this proportionately to the height. Who will have the equation? The change in pressure over the change in height is you go to K times p herpes. The pressure. We know that at sea level at height is equal to zero p. Zero Pressure is 101.3 k p a. I wondered in 1.3. Okay. We also know that at 1000 meters at P of 1000 but the pressure is equal to 87 0.14 Keep you. We can integrate both sides of this differential equation. We'll get our exponential growth function, which states the pressure is equal to the initial pressure. Times e raised Katie. Sorry. Erased the K Times HQ. We're talking about height. In this case, you can plug ins and values and figure out what Caisse? You know that our pressure at 1000 87.14 You know that our initial pressure is 101.3 that occurs when at sea level are no height. He raised to the kh Okay, we're finding h is 1000. That is the height corresponding with the 87.14 kilo Paschal's I Don't want to solve for K. We have 87.14 Divide both sides by 101 0.3. Does he go to e to the 1000 k? We don't hate the natural log of both sides. You're left with the natural law, a 7.14 over 101.3 Ln and the you will cancel 1000 k Okay, It's simply one one Thousands times the natural law, a 7.14 over 101 0.3 beds. Your 100. And once there we go. Hopefully that algebra we can find that we get a value of K be very small. Negative 0.0 15 06 It's now we know that our equation becomes pressured. Any height, pressure for any height. Siegel to our initial pressure, which is still 101.3 times he raised to the negative point 000 1506 times h times. When you're asked to figure out pressure at 3000 meters for party per day now that we have a height of 3000 meters. It was like that into the equation. P of 3000 0 201.3 erased the negative 0.15 or six times 3000 and we do that calculation we get and value of 64 0.5 Paschal's So we got the pressure at 3000 meters is approximately 64.5 que a basket. Next we're asked to find the pressure on the top of Mount McKinley and MAV A killing has an altitude of 61. 87 meters. Again, let's plug it right in p of 61 87 about 201.3 times erase the negative 0.1506 times 61 87 and that comes out to 39.9. That is again in killing Paschal's. We have an answer of P of 61 87 meters, Ziegel to 39.9 39 point Paschal's, and that is our answer. Thanks for watching

View More Answers From This Book

Find Another Textbook

In mathematics, precalculus is the study of functions (as opposed to calculu…

In mathematics, a function (or map) f from a set X to a set Y is a rule whic…

The rate of change of atmospheric pressure $ P $ with respect to altitude $ …

Atmospheric pressure The earth's atmospheric pressure $p$ is often mode…

The atmospheric pressure $P(h)$ (in kilopascals) at a height $h$ meters abov…

Atmospheric Pressure Atmospheric pressure $P$ (in kilopascals, kPa) at altit…

Physics At a constant temperature, the atmospheric pressure $p$ in pascals i…

The atmospheric pressure at altitude $h$ (kilometers) for $11 \leq h \leq$ 2…

Atmospheric Pressure $\Leftrightarrow$ Atmospheric pressure $P$ (in kilopasc…

Atmospheric pressure $P$ (in kilo-pascals, kPa) at altitude $h$ (in kilomete…

Air pressure, $P$, decreases exponentially with height, $h$ above sea level.…

The altimeter in an airplane gives the altitude or height $h(\text { in feet…

Atmospheric pressure The pressure of Earth's atmosphere at sea level is…

The atmospheric pressure $p$ on an object decreases with increasing height. …

Modeling Data The atmospheric pressure decreases with increasing altitude. A…

Approximate the change in the atmospheric pressure when the altitude increas…

The atmospheric pressure $p$ on aballoon or airplane decreases with incr…

When air expands adiabatically (without gaining or losing heat), its pressur…

When air expands adiabatically (without gaining or losingheat), its pres…

02:38

Find the limit.$$\lim _{x \rightarrow \infty} \frac{2+10^{x}}{3-10^{x}}$…

04:38

The circumference of a sphere was measured to be 84 $\mathrm{cm}$with a …

Differentiate the function.

$$f(x)=\sin x \ln (5 x)$$

01:17

$1-38=$ Find the limit. Use l'Hospital's Rule where appropriate.

Find an equation of the tangent line to the curve$y=\sqrt{3+x^{2}}$ that…

06:30

$11-14=$(a) What quantities are given in the problem?(b) What is the…

01:07

Use a linear approximation (or differentials) to estimate the given number.<…

01:15

Find the derivative of the function. Simplify where possible.$$g(x)=\sqr…

05:15

A freshly brewed cup of coffee has temperature $95^{\circ} \mathrm{C}$ in a<…

01:35

$43-46=$ Find the first and second derivatives of the function.$$y=\cos …