• Join over 1.2 million students every month
• Accelerate your learning by 29%
• Unlimited access from just £6.99 per month
Page
1. 1
1
2. 2
2
3. 3
3
4. 4
4
5. 5
5
6. 6
6
7. 7
7
8. 8
8
9. 9
9
10. 10
10
11. 11
11
12. 12
12

# Crows Dropping Nuts

Extracts from this document...

Introduction

Min Hua Ma

9-18-09

IB SL MATHEMATICS

Internal Assessment

Type II

IB SL Type II Internal Assessment: Crows Dropping Nuts

This assignment is an investigation to find a function that models a given set of data. By using various methods, such as matrixes, different types of regressions, and technology, it allows the investigator/student to create various equations to model the data. This assessment is about birds dropping different sized nuts on a hard surface in a range of heights in order to break open the shells. There are three variables in this investigation: the size of nuts, the heights of drops, and last but not least, the number of drops.

The first set of data is on crows dropping large nuts:

 Height of drop 1.7 2 2.9 4.1 5.6 6.3 7 8 10 13.9 Number of drops 42 21 10.3 6.8 5.1 4.8 4.4 4.1 3.7 3.2

To begin this investigation, I began plotting the given points on a scatter plot:

Then, I decided to begin with using matrixes to formulate an equation. I wanted to do a matrix using all the points to create this polynomial:

ax9+bx8+ cx7+dx6+ex5+fx4+gx3+hx2+ix+j

I put all the y values in matrix [A] and all the x values in matrix [B].

Middle

This equation models the points of the last 5 data, but is very close for modeling points 2 and 5.

Subsequently after using matrices, I realized that using polynomial equations won’t help model the given data since both polynomial equations create a parabola not a decaying model. So I decided that using matrices wasn’t a good way to model the data. I began looking at ways to form to model decay. Using the GCD, I started with using PwrReG.

To find the formula using PwrReg, press STAT, go to CALC, scroll down to A, and enter again. This will bring the calculator to the main screen with PwrReG, so now press enter again. Then the screen will give the values of “a” and “b”. Plug the information into (y=) and press (GRAPH).

Looking at the graph, this function shows decay and the equation is very close to all of the data, but only goes through the 2nd and 8th point. The regression of the equation is -.95.

After that, I used the calculator again to find ExpReG. Using the method as the PwrReG, I got the equation:

Y=21.37241705 x (.8358432605x)

Using the given function I plugged in the equation and got:

Conclusion

)-1.2

Small Nuts: y= 37.67398021 x (.894911559191.5x + 2.5) +4

Also, by inferring to the equations above, I see that the medium and small nuts have greater number of drops in order to break open than the large nuts.

My first model: Y=20.04386 • (.836011610x) + .5 doesn’t replicate the data of medium and small size nuts because the data from the large nuts had a different heights than both of the small and medium size nuts. The decay equation from the first model is much steeper than the other two. In order to adjust the model to fit the smaller sizes, I first began by making the heights the same, and then compared the ExpReG of each. Even though the heights are the same, the numbers of drops for each of the different sizes of nuts aren’t very similar, so making the first function be able to model the medium and small nuts isn’t very likely. In addition, the regressions of the medium and small nuts aren’t very strong, given that they only model 2 of the 8 points from the data. The limitation in this investigation is: there just can’t be any size for a nut. For example, there can’t be a negative height, some heights aren’t able to break nuts, and the size of nuts must be too large or too small so a seed can’t be 10 pounds.

Ma

This student written piece of work is one of many that can be found in our International Baccalaureate Maths section.

## Found what you're looking for?

• Start learning 29% faster today
• 150,000+ documents available
• Just £6.99 a month

Not the one? Search for your essay title...
• Join over 1.2 million students every month
• Accelerate your learning by 29%
• Unlimited access from just £6.99 per month

# Related International Baccalaureate Maths essays

1. ## Tide Modeling

And it was assumed that the other points in the graph would consequently be as accurate as those two specific problems. All that work can be seen when analyzing the chart below. The points were grouped by two because those are the frequencies in which the period repeats itself, further

2. ## A logistic model

run r ? ?3.8 ?10?5 u ? 3.28 n n ? un?1 ? (?3.8 ? 10?5 u n ? 3.28)un ? (?3.8 ?10?5 )(u )(u ) ? 3.28u The logistic function model for un+1 is: n n n ? (?3.8 ?10?5 )(u 2 ) ? 3.28u ?5 2 un?1 ?

1. ## Crows dropping nuts

may not lie on the data points given, and this may go to partly explain any variations between the fitted curve and the data points, even if it is only a small effect. The model given for both h and n will be the fit for discrete data, whereby there is a variation in the variables.

2. ## Population trends. The aim of this investigation is to find out more about different ...

only difference would be that the curve of would take longer to stay at the same amount of population. This model is of equation , the number 250 is there only to increase the size of the curve and for it to be visible to such a scale.

1. ## Creating a logistic model

1.962 2 45126 1.386724 3 62577.30722 0.932990012 4 58384.00263 1.042015932 5 60837.06089 0.978236417 6 59513.02846 1.01266126 7 60266.53839 0.993070002 8 59848.89139 1.003928824 9 60084.02714 0.997815294 10 59952.76123 1.001228208 11 60026.39569 0.999313712 12 59985.2003 1.000384792 13 60008.28214 0.999784664 14 59995.36022 1.000120634 15 60002.59772 0.999932459 16 59998.5451 1.000037827 17 60000.81469 0.999978818 18

2. ## IB Math Methods SL: Internal Assessment on Gold Medal Heights

187 191 195 199 203 207 212 216 220 224 228 232 236 * - Although there are values for 1940 and 1944 (8 and 12 years elapsed respectively); as the original data set does not have such data for those years, we reject the two h-values.

1. ## In this Internal Assessment, functions that best model the population of China from 1950-1995 ...

However, starting at the 4th data point, or year 2000, the curve and the data points shift away from each other in different directions. The curve extends toward infinity at a steady rate of change while the data points slow down in their rate of change and near and asymptote.

2. ## Gold Medal heights IB IA- score 15

This disables the understanding of where the graph is located in relation with the origin. However, the graph is chosen to be represented in this manner because it helps the viewer visualize the relation between the year and the height jumped.

• Over 160,000 pieces
of student written work
• Annotated by
experienced teachers
• Ideas and feedback to