IB Math Methods

Mathematical Modeling Project

Suppose that the person in charge of the soda machine at school wants to find how many quarters are collected without counting every quarter. Devise a Mathematical model that would allow him/her to find the number of quarters deposited based on total weight of the quarters.

Procedure:

Place 1 US quarter coin on a digital balance and record its weight, place another quarter on top of the first and record the weight for the 2 coins. Repeat this process until all 8 quarters are weighed.

Number of Coins(Y)	1	2	3	4	5	6	7	8
Weight of coins(X)

a)      Plot the points in the table above. Does the data represent a perfectly linear model? Explain

b)      Find an equation of the least squares line which will allow for the prediction of the number of coins given its weight

c)      Is there a positive correlation or a negative correlation involved?

d)      Complete the following table:

Exact Weight of Coins(x)	Exact Number of Coins(y)	Predicted Number of Coins (Given by Model)(y)	% Error
	1
	2
	3
	4
	5
	6
	7
	8

e)      What are possible limitations/errors involved in this experiment?

f) How effective is your model?