• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

Math-gradient function

Extracts from this document...

Introduction

GRADIENT FUNCTION

The aim of this assignment is to find the relationship between the gradient function. For this assignment I will use the height of drops and the number of drops needed to crack open nuts of different sizes; large, medium and small. The models are then compared in terms of the usefulness of the models.

The table below shows the average number of drops it takes to break open large nuts from varying heights.

Large nuts

Height of drop (m)

Number of drops

  1.7

42.0

  2.0

21.0

  2.9

10.3

  4.1

  6.8

  5.6

  5.1

  6.3

  4.8

  7.0

  4.4

  8.0

  4.1

10.0

  3.7

13.9

  3.2

Let (h) metres be the height of drop and (n) be the number of drops. The graph below is of n against h

image00.png

...read more.

Middle

                                                                        (ax+b)

By use of GDC, geogebra i found the equation by moving the line of the curve to fit accurately.  1 ÷ (0.06x+0.012)-0.08) +1.48

image01.png

Another function that models the data is the logistic function. This is because it has a horizontal asymptote of 0.

image02.png

             3.6          

1-1.55e^ (8-0.31x)

 The difference between the reciprocal function and the logistic function is that the logistic function fits more accurately. However, it is still hard to predict other values from the equations

The table below shows the

...read more.

Conclusion

ebra/gradient_function/889634/html/images/image03.png" style="width:580.93px;height:431.93px;margin-left:0px;margin-top:0px;" alt="image03.png" />

image04.png

The logistic equation f (n) for medium nuts= -0.26÷(1-0.99e^0.01x)

Small nuts

Height of drop (m)

Number of drops

  1.5

Undefined

  2.0

Undefined

  3.0

undefined

  4.0

  57.0

  5.0

  19.0

  6.0

  14.7

  7.0

  12.3

  8.0

    9.7

10.0

  13.3

15.0

    9.5

image05.png

image06.png

1/(0.02x-0.08)

image07.png

The equation for logistic function f(n) for small nuts is

10.62÷ (1.897e^ (-0.6x)

The first model does not fit the data accurately for nuts of different sizes and it is therefore hard to predict a trend from this. The models were unable to predict undefined values and this were therefore the limitations.                                            

...read more.

This student written piece of work is one of many that can be found in our GCSE Gradient Function 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

See related essaysSee related essays

Related GCSE Gradient Function essays

  1. Peer reviewed

    The Gradient Function Coursework

    5 star(s)

    Calculus often deals with the following topics: 1. How to find the instantaneous change (called the "derivative") of various functions. (The process of doing so is called "differentiation".) 2. How to use derivatives to solve various kinds of problems. 3.

  2. The Gradient Function

    To find the next set of co-ordinates is simple. You just have to make the points that you have just worked out a bit more accurate. This means that it will now be 0.81. Once again you have to multiply this by 3.

  1. The Gradient Function Investigation

    Testing and Proof I need to test (by trying my rule for different graphs), and then prove, my rule. To prove my rule I will need to work through the 'small increments of size "h" method' with the hypothetical graph equation y = Axn.

  2. Maths Coursework - The Open Box Problem

    After choosing 3 different cut outs for the square I constructed a general table. Size of Square Length of cut out which maximises volume 10 by 20 1.6 recurring 20 by 20 3.3 recurring 30 by 30 5 After analyzing the results I discovered a relationship between the length of

  1. Gradient function

    35.7604 -0.2396 -0.01 23.96 2.999 35.976 -0.023996 -0.001 23.996 3 36 0 0 0 3.0001 36.0024 0.00240004 0.0001 24.0004 3.001 36.024 0.024004 0.001 24.004 3.01 36.2404 0.2404 0.01 24.04 3.1 38.44 2.44 0.1 24.4 3.2 40.96 4.96 0.2 24.8 3.3 43.56 7.56 0.3 25.2 3.4 46.24 10.24 0.4 25.6 3.5

  2. Gradient Function

    change in x gradient 2 12 15 1 15 2.1 13.23 13.77 0.9 15.3 2.2 14.52 12.48 0.8 15.6 2.3 15.87 11.13 0.7 15.9 2.4 17.28 9.72 0.6 16.2 2.5 18.75 8.25 0.5 16.5 2.6 20.28 6.72 0.4 16.8 2.7 21.87 5.13 0.3 17.1 2.8 23.52 3.48 0.2 17.4 2.9

  1. The Gradient Function

    If this gradient function, 4ax3 is correct, then the gradient function of 10x4 will be 40x3. To prove that it is 40x3 I am going to draw up a table of values for certain x values. For the curve y=10x4, using the gradient function 40x3 I think the gradients will

  2. The Gradient Function

    1 -1 2 1 -2 2 -1 4 -0.5 Gradients: L1: Gradient at point X = -2 Y2-Y1 X2-X1 = 1.375-0.75 = 0.66 -1.4-(-2.35) L2: Gradient at point X =2 Y2-Y1 X2-X1 = -0.8-(-1.25) = 0.75 2.25-1.65 L3: Gradient at point X = -3 Y2-Y1 X2-X1 =-0.625-0.5 = 0.15625 = 0.16 rounded to 2.d.p -3.05-(-3.85)

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