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IA Crows dropping nut

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ok guys im kinda doing my second portfolio right now n im kinda stuck on one part of the question

height 1.7 2.0 2.9 4.1 5.6 6.3 7.0 8.0 10.0 13.9

number of drops 42.0 21.0 10.3 6.8 5.1 4.8 4.4 4.1 3.7 3.2

they given us information on crows dropping nut.. with the height and the number of drops.i managed to plot this graph n i get an Hyperbole graph. the question asks

what type of function models the behavior of the graph? explain why you chose this function.create an equation (a model)that fits the graph.

i dont get how to get the equation they asking for. please could someone help me urgently..or explain to me.thanx

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It looks like you're dealing with a decreasing exponential curve, I'd try modelling it to y = Ae^-kx and see what comes up. A should be the value of x where the graph crosses the y-axis, and k should be chosen so that it matches the curve of your data. Alternatively, just get a computer graphing program to look for the solution.

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Frankly speaking: I would recommend TI Interactive! or Graphical Analysis, as they can serve better than GeoGebra, judging by my own experience. Do bear heed that this is a subjective opinion, nevertheless the advice can safely be used - seeing that I got 18/20 points awarded on the exact same portfolio task.

Best of luck.

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It looks like you're dealing with a decreasing exponential curve, I'd try modelling it to y = Ae^-kx and see what comes up. A should be the value of x where the graph crosses the y-axis, and k should be chosen so that it matches the curve of your data. Alternatively, just get a computer graphing program to look for the solution.

That makes no sense. The function will never cross the y axis, you can't logically have a negative height in this experiment

It's going to be a rational equation.

To get the closest possible eqn, just do a power regression in your calc. It has to be something along the lines of y=(a)(x^-n)

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*sigh*...c'mon guys, kristers so far is the closest, though not even close. I don't want to go over the entire IA again but i'll give you simple things to look for:

1. this is an experiment testing gravity, meaning that you want to have a reciprical function (not an exponential because you can't have negative height!!!) and for those in physics you should know that gravity works most of the times as a square reciprical? so look for a function where its 1/x^something between 1 and 2.

2. you need to use parameters and technology: to tell you the truth, no graphying program will give you a better result than graphing it yourself, and yes, kristers was in the right track, but he was missing 2 parameter.

parameters: a(x-b)^-c + d and think about what each of these parameters do (obviously d will giveyou a horizontal assymptote so think about what happens as height goes to infinity...number of drops goes to...0? it takes 0 times to open a nut from infinity height? hint hint, probably one :P ), c is your rate of fall so play around with that, a softens the curvatue of your drop, kinda like c, and b is a shift...again think about what your minimum x value should be.

3. IT IS NOT AN EXPONENTIAL FUNCTION

4. doing a power regression in your calculator is a good idea but just know that playing aroudn with the four parameters by yourself will give you a much better graph, I got it to match all of them perfectly.

5. I'm gonna go watch House now cause I need to finish my WL1 but I rather watch something educational than write bul**** for six hours. House is an ******* but I wanna group up to be just like him, except for the leg part, I like running, I already have the sarcasm down...

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That's completely wrong... an exponential function models the curve almost perfectly.

42 exp[secret] is extremely close to the data points, and I did that one by hand on a piece of scrap paper... the function itself can cross the y axis, since it's not an exact science, and because the function can be defined to have y as positive. That being said, polynomial functions can get close, but an exponential function will probably get you closer, since this appears to be continuously decreasing curve, which can be represented by a rational function or an exponential one, both have an asymptote at y=0, and since there are no data points to the left of 1.7 you could use both curves to model the function.

Edited by deissi

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That's completely wrong... an exponential function models the curve almost perfectly.

42 exp[secret] is extremely close to the data points, and I did that one by hand on a piece of scrap paper... the function itself can cross the y axis, since it's not an exact science, and because the function can be defined to have y as positive. That being said, polynomial functions can get close, but an exponential function will probably get you closer, since this appears to be continuously decreasing curve, which can be represented by a rational function or an exponential one, both have an asymptote at y=0, and since there are no data points to the left of 1.7 you could use both curves to model the function.

Ok, I guess you're right. Though who's gonna break the news to Newton and tell him that his equations for the laws of gravity were all wrong? You should go tell him that an exponential function is in fact better than his theory of squarely inversevly proportional gravitaional forces and show him how you did an IB paper on nuts falling of the sky where an exponential function graphs the data points much better than anything he ever proved. Maybe we should go to Einstein too and let him know that E doesnt equal MC^2 as well as M*e© does so we should throw away the theory of special relativity.

Just becasue something seems nicer on paper doesn't exactly mean it's the way things behave in reality. From this paper alone and if you're really really close minded you might be able to get confused and use an exponential function seeing as how the data fits so well. But in real life, the phisics of gravity don't work exponentially. So don't tell me I'm completely wrong unless you've taken some weird physics class that can prove me wrong.

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News flash. Gravitational forces vary by extremely small amounts when you increase or decrease height by anything short of a few hundred kilometers. If you're talking about time to reach the ground, then state that, though I don't know where the "number of drops" would account for that.

Anyways, I hadn't read the portfolio itself, so I assumed that height and number of drops were the behavior patters of crows and nothing to do with physics at all. I see alot of exponential curves in bio so that's what I suggested. I just checked with an inverse square function and it models it pretty nicely as well, though the exponential one got closer so far.

EDIT

Just looked through the IA, and yeah, it looks like I'd take an inverse function, simply because you would never break the nut open at 0 meters. That being said, the horizontal asymptote will probably not be one, simply because it reaches a max speed while falling.

Edited by SharkSpider

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This is my first attempt at a Type II portfolio and I have completed the objective, however my teacher told me that I`ll get more points for going off on a reasonable tangent. I'm not exactly sure what this means. The portfolio seems to be fairly short. It asks me to find two equations that model the data, which I have done. How do I .. go further? Anyone care to elaborate?

Edited by o1.Danniiee

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I am doing the same thing...maybe you could go into the physics of the crows dropping nuts...like the GPE and KE and how it changes with mass and height (obviously the gravitational force does not change a significant amount so you won't need to take that into consideration)...what type of equation did you make? (exponential, logarithmic,etc.)

by the way, this is my first IA ever, so if you have any cool ideas please let me know

what score are you aiming for?

Edited by thinkgreen95

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That being said, the horizontal asymptote will probably not be one, simply because it reaches a max speed while falling.

How is the horizontal asymptote not one? The nut cannot break after being dropped less than one times. In other words, you have to drop the nut at least once in order for it to break... how is it not one?

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My teacher gave me a score of 18 w/ a plus or minus 1 prediction. I don`t think you need to go into detail the physics of it, just stick to the portfolio math. One of the most useful things I found to do was to make predictions with my model to see if the GDC's or mine was more accurate.

My model was a polynomial rational.

Edited by o1.Danniiee

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Once you get the equation of the trend line, how do you establish what type of function it is for example, exponential or logarithmic ect?

Once you get the equation of the trend line, how do you establish what type of function it is for example, exponential or logarithmic ect?

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Once you get the equation of the trend line, how do you establish what type of function it is for example, exponential or logarithmic ect?

Once you get the equation of the trend line, how do you establish what type of function it is for example, exponential or logarithmic ect?

If you run a regression you could easily find out which ones fit the data the best, or you could just use elimination and decide which equations would fit the shape of the graph.

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ezex could you explain what type of function a(x-b)^-c + d is? is it reciprocal? polynomial? i've got it to fit perfectly but i can't use it in my coursework as i cant work out what type of function it is! cheers in advance!

oli

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im doing the crows dropping nuts and honestly i dont even know how to graph this on my calculor

and wat are parameters and wat are the variables?

thanks

Variables are basically x and y. They're the things that are being measured, like height, speed, time, amount of something, and so on.

Parameters are constants that affect the overall general function. So, for example, the general function for a polynomial is ax^2 + bx + c, right? The parameters are a, b and c. Another example: the general function for a sine graph is y = a sin (bx+c) + d. The parameters are a, b, c and d. Get it now? Hope that helps!

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Variables are basically x and y. They're the things that are being measured, like height, speed, time, amount of something, and so on.

Parameters are constants that affect the overall general function. So, for example, the general function for a polynomial is ax^2 + bx + c, right? The parameters are a, b and c. Another example: the general function for a sine graph is y = a sin (bx+c) + d. The parameters are a, b, c and d. Get it now? Hope that helps!

oh my god that helps so much! thank you :)

but i have another question...when you begin the paper and you're supposed to write an introduction or something, what are you supposed to write?

Just what the paper will discuss or something?

thank you soo much!

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