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

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Introduction  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.

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

Conclusion 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.

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

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