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Air pressure may be represented as a function of height (in meters) above the surface of the Earth, as shown below: OO012h P(h) = PoIn this function, Po is the air ...

Question

Air pressure may be represented as a function of height (in meters) above the surface of the Earth, as shown below: OO012h P(h) = PoIn this function, Po is the air pressure at the surface of the Earth, and his the height above the surface of the Earth; measured in meters: Whichoexpression best represents the air pressure at an altitude of 3,000 meters above the surface of the Earth?3,000e ,0.00012Po Po/e0.36 C. Poe 3,000 Poe0,36

Air pressure may be represented as a function of height (in meters) above the surface of the Earth, as shown below: OO012h P(h) = Po In this function, Po is the air pressure at the surface of the Earth, and his the height above the surface of the Earth; measured in meters: Whichoexpression best represents the air pressure at an altitude of 3,000 meters above the surface of the Earth? 3,000e ,0.00012Po Po/e0.36 C. Poe 3,000 Poe0,36



Answers

Atmospheric pressure Under certain conditions the atmospheric pressure $p$ (in inches) at altitude $h$ feet is given by $p=29 e^{-0.000034 h}$. What is the pressure at an altitude of A. $30,000$ feet? B. $40,000$ feet?

So in this question we're dealing with exponential functions and part A is just a matter of taking the values and plugging them into your graphing calculators. So there's not actually too much maths involved the burrito that out and your graph should look something like this. And so you can see there is pressure on the Y axis, altitude on the X axis. Because we would say altitude is a independent variable on pressures, the dependent variable. So I will just make that a bit smaller and leave it over here. So for part B. Then we're deciding whether an exponential line or a linear line would best describe this graph that we have here. And if you can see at the bottom of the line, you have a little bit of a curve. Now that's hinting that it would be an exponential grass, specifically an exponential function to a negative powers. They would have E. To the minus ex. Not something like that. Um Because a linear, you had a linear one, it would be completely straight like that. You wouldn't have this curve here at the end. So you say for B. Mhm. We'll have down just put down exponential. Dad part C. Again is just taking taking this s today estimation. Sorry for the graph P F X is equal to one zero one three. Yeah. By E as I remember I said about the negative exponent zero point zero zero shero one three for X. And again, I've already done this bed. So you can see what it looks like when you put it into your graph. So you should get something like this. And as you can see the graph of the scatter plot and the graph of the estimation are very similar. The fuck up here. And then party is just subbing in values for X. So you have so that's part C. And then party you're just taking this function. And you're saying well what's the value of P at X. Is equal to 1500. So your trust changing this X. Here to 1500. Or for the next part? 11,000. Yeah. So people to 1013 by E. To the power of finest shero point 00 Sarah one three four. Bye. 1000 500. And when you plug that into your calculator, you'll get that is roughly equal two 828. And then you do the same for X. Is equal to 11,000. So you're just doing the same thing again. But instead of 1500 here you'll have 11,000. And when you plot that into your calculator, you get that is roughly equal 2 232. Yeah. So now we're comparing these values two right? The values of 846 and 227? Yeah, so these are pretty similar. Um They're not exact. Uh And you could say that sure to to step your 2 to 7 is closer to 232 So it seems starting. That implies that this estimation gets bigger for larger value. The sorry, the estimation gets more accurate for larger values of acts. You don't really have enough detail to say that definitively. Um But yeah, there close enough. It could be better, Yeah, there is potentially a different formula for P. F. X. That would give you a more accurate result, but it's somewhere it's on the right track essentially.

This question asks us to determine the air pressure and what the air pressure is at the given height. What we know is that we can take our P formula, which is pivo our initial value times E to the negative 0.12 on the multiply this by our height in meters, which we know it's 6194 We end up with 0.4755 which could be written as a percentage as 47.55%. This is our percent value for part a now moving on to part B. What we know is that we could figure out p of 12,000 which means we have p of o E to the negative 0.12 times 12,000. As you can see, we are going to end up with a percent value of 23 points. Seven and this is in terms of

This problem, we are given that the atmospheric pressure at an altitude of H feet is given by the formula P. Is april 29 E. To the negative zero 346 H. And we would like to find the pressure at an altitude of 40,000 ft. Now in here, H is our altitude P. Is the pressure. And on this specific problem we were told that H Is equal to 40,000. And so that just amounts of plugging in 40,000 into this formula for h. And then finding what he is. So P is 29 e. to the negative .0000346. Yeah. Times 40,000. Yeah. And from here we can just type this exactly like it looks on a calculator and you may want to be a little extra careful foot double prints. Is there in that experiment? That way. All of it ends up in your next month. But again, we can just type this in exactly like it looks, you know, attacked later. And when we do that, our output Should be 7.44. So that tells us our pressure is 7.44.

So we're given this equation for pressure And given that the pressure at sea level is equal to £14.. inch squared where we have a being the altitude at which the pressure is calculated. And for our first problem, we want to find the pressure at an altitude of 1000 ft. So we'll solve for a being equal to 1000 ft. We plug this into our equation knowing that are a value and our pressure at sea level. Our equation should look something like this with our values plugged in. Now we'll plug this into our calculator and solve for P. We find P equal 2 13 0.98 or mhm 14 £14 per inch squared at 1000 ft. That's the pressure. If we want to find the pressure at an altitude of 20,000 ft, we'll do the same thing and notice that the number that we're changing here, this a value we're changing here is affecting R. E. Exponents, right? So will notice the change in altitude and how that ends up affecting our pressure. So we'll plug those numbers back in except instead of 1000, we have 20,000. And we plug this into our calculator. We come up with 5.4 one pounds per inch squared. That's our pressure at an altitude Of 20,000 ft. Now, if we're looking for at what altitude the pressure Is going to be equal to 14.7 pounds per inch squared. Well, we already know that. Right? We calculated that already because this was our given pressure at sea level where we started our equation and at sea level our initial pressure we used a was equal to zero. Okay, you can also prove that by just substituting in 0.7 13.7 E. The rest of our values here and solving for a to find our rate of change then of pressure. We take our derivative here. Just end up with thank you. 14 0.7 times a negative 0.5 Can't- .00073 five. So if we say D. P. D. A. The rate is equal to our value here. Were saying that the change in pressure. No, you don't care. Uh huh. This is our rate of change of just the pressure.


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