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

Collect data and investigate whether it can be model by a exponential function

Extracts from this document...

Introduction

image00.png

image01.png

Introduction

We were required to analyse a set of data and write a report on it. we had to either find a situation which we had to negotiated with our teacher, that you fell might be able to be a modeled by an exponential function OR given a alternate situation by our teacher. I did the Alternative situation

Part A

The aim of this assignment was to collect data and investigate whether it can be model by a exponential function

1)

DATA

X (height) Y (time)

2.5         3.45

5            6.12

7.5         9.45

10          13.35

12.5       17.39

15          22.87

17.5       27.97

20          34.45

22.5       44.12

25          64.23

The data that I have collected is from a 1.5 liter coke bottle that has been measured from top to bottom. The height of the bottle was measured to 25cm. I interval that I measured in was 2.5 cm, which gave me 10points for my graph.

...read more.

Middle

3.4298*0.119^x. but both of the equation fits the data nearly perfectly. So therefore I don’t know which one is the right equation, but the equation I will be using will be the first one which is 3.429801*1.126417^x.

3) Validating

I used Excel to Validate. I added a trendline to my equation

Part B

Yi+1 – Yi versus X graph

This is the graph of Yi+1 – Yi versus X. as you can see from the graph you can tell that this is going to be an exponential function. Interpreting the graph you can see it is almost the same as the original graph. There is a gradual increase in the last section of the graph the reason for this is because of the huge increase in time between 25 cm and 22.5 cm. The equation for this graph is 1.961621*1.088371^x

...read more.

Conclusion

image04.png

 To find a equation to fit this graph you can use the Graphics Calculator. Using the Math function on the Data Matrix Editor. It will give you equation of  0.406336*1.126693^x.

Part D(Complex Applications)

Looking at the equation from part b and c there is not really thing that is similar thing. Both of the equation have not really much in common except that for ‘b’ is greater than 1.

The reason for a big gap in the equation between part c and b is because that the instantaneous rate of change is only added by a small number (e.g.  0.0001) and therefore does not make much of a difference, but in part b which you have to find the Yi+1-Y1 which is greater which means the initial value (which is a)will be greater than b.

In conclusion you can draw it is possible to model a exponential function on this assignment.

...read more.

This student written piece of work is one of many that can be found in our AS and A Level Core & Pure Mathematics 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 AS and A Level Core & Pure Mathematics essays

  1. Marked by a teacher

    The Gradient Function

    5 star(s)

    Here, it is a little hard to prove this in the normal sense as (x+h) is square rooted, so I will need to rationalize the numerator. V (x+h) - Vx = V (x+h) - Vx x + h -x h V (x+h)

  2. Marked by a teacher

    Estimate a consumption function for the UK economy explaining the economic theory and statistical ...

    3 star(s)

    This absolute value should be the higher the better. T- values in this case not as high as we want, they are 4.57 and 119 respectively. In order to estimate more precisely, DW (Durbin- Watson) can be considered. DW equal to 0 if there is extreme positive serial correlation.

  1. Determine an appropriate parabolic model that fits the data I collected of whirlybird wing ...

    As a gets closer to 0 the parabola becomes wider. Below the final quadratic function, Y= -0.033(X-8.5)2+2.33 is superimposed onto my original data points. In the tables below, the results when the different lengths are substituted into the function, can be compared with our initial data table.

  2. Three ways of reading The Bloody Chamber.

    The sort of understanding that is required of the reader is one in which both the first and second order readings are presupposed and gone beyond. It therefore requires a certain knowing ness on the part of the reader. A recognition that a mythic or a Freudian interpretation is not

  1. Estimate a consumption function for the UK economy explaining the statistical techniques you have ...

    the proportion of personally disposable income consumed, such as in the early 1970s and early 1980s. Evidence suggests that the Keynesian consumption function could not resolve these problems and there was need for a more accurate consumption function. This led to many attempts to estimate an equation, which can predict

  2. Maths - Investigate how many people can be carried in each type of vessel.

    We now take the newly formed equations (iv) and (v) and we will now eliminate one of the factors from them. 25y + 2z = 133 X2) y - z = 1 => 2y - 2z = 2 27y = 135 y = 5 Now that we know one of the factors, we will now start to utilise the technique of substitution in our problem.

  1. Investigation of the Phi Function

    = ?(7) x ?(4) ii ?(6 x 4) = ?(24) = 8 ?(6) x ?(4) = 2 x 2 = 4 Therefore, ?(6 x 4) = ?(6) x ?(4) b) Check whether or not ?(mn) = ?(m) x ?(n) for at least two separate choices of n and m i ?(5 x 10)

  2. Math Portfolio Type II - Applications of Sinusoidal Functions

    Calculate the vertical stretch factor that would be required in the transformation of the graph of function f into the graph of function g. The amplitude that represents the time of sunrise in Toronto is 1.627 and the amplitude that represents the time of sunrise in Miami is 0.846.

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