help im struggling with the remaining questions ! its urgent

Question

1. At the beach in San Francisco (0 meters) the pressure of the atmosphere is 101.325 kPa

(kilopascals) and in Denver, 1609.344 meters above sea level, the pressure of the atmosphere

is about 83.437 kPa. Using this data, find a linear equation for pressure P in terms of

altitude h. (Hint: write the pressure and altitude in each location as a point (h, P). Then

use point-slope form to find the equation of the line.)

answer :

2. What is the rate of change of the pressure of the atmosphere as altitude increases in meters?

Write a sentence answering this question using the phrase “rate of change.”

3. Mount Everest is 8848 meters high. What does your linear approximation predict for the

pressure of the atmosphere on Mount Everest?

4. Compared to San Francisco, how much oxygen is available in a breath of air in Denver? Since

21% of the molecules in the air are oxygen molecules in either situation, we can just compute

the ratio P(Denver)/P(SF)

5. Using the same technique as question 3, express as a percentage how much oxygen is available

in a breath on Mount Everest as compared to San Francisco.

 

6. Let’s do a very basic check of whether our linear model is good. What would it mean for

the pressure of the atmosphere P(h) at an altitude h to equal zero?

7. Does our model indicate that P(h) will equal zero at some altitude? If so, P(h)=0 at what

altitude?

8. The air pressure at the peak of Mount Everest is actually closer to 31.5 kPa. Draw some

conclusions about the validity of our model.

Answer 1

Hi,

Since you seem to be pressed for time, I'll submit the answer to some of the questions a few at a time.

First, in Question 1, you need to check your subtraction to be sure you didn't make a typo in the numerator of the slope (101.325 - 83.437 does not equal 17.978).

Secondly, that fraction is not reduced (you might notice the numerator and denominator are both even, so they have a common factor of 2, at least). Slope needs to be in simplest form.

In Question 2, you are asked to give the rate of change in the context of the problem. Rate of change is the same as the slope. So, your answer should be a sentence such as: For every meter the altitude increases, the rate of change in pressure in the atmosphere is __put your slope here__.

In Question 3, to find the pressure of atmosphere for Mount Everest, plug in the height of Mt. Everest (8848) where h is in your equation (in Question 1) and solve for p.

Hope this helps.

NOTE: I'm not sure if you can see my additional comments, so I'm copying-and-pasting them here:

 

 In Question 4, follow the second sentence, and just put the pressure at Denver (83.437) over the pressure at S.F. (101.325) to make a fraction. This fraction will be the ratio of the two pressures. The ratio of oxygen will be the same as the ratio of the two pressures.

 

 In Question 6, let p equal 0. What would h be, if p = 0? What would this mean in the real world (in the context of this problem)? Where would the pressure of the atmosphere be zero?