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DEVELOPING EXPERT VOICES Applied Math 40s 2007 CREATOR:   JENNIFER Question 1 : Matrices
[object Object],Hello everyone! My name is Jennifer and I’m taking an Applied Math 40s course. Well here is my Developing Expert Voices project. I worked really hard on it so I hope you guys enjoy and learn a few things from it! Okay ENJOY! ,[object Object],My project will consist of 4 different mathematical questions. I will be focusing on 3 units of Applied Math 40s. I will create questions that relate to Matrices, Statistics, and Probability. My project will be presented on Slideshare so I hope you guys enjoy it!
MATRICES:  Question 1 A construction work base has a workforce of 1820 people, with 1640 employed, and 160 unemployed. In one year 10% of employed workers will lose their jobs, and 70% of unemployed people will find jobs. ,[object Object],[object Object],[object Object],[object Object],[object Object]
MATRICES:   Answer – Q.1 Part A ,[object Object],This matrix indicates the present situation, where 1640 people are employed and 160 people are unemployed.
[object Object],MATRICES:   Answer – Q.1 Part B OR b)  Construct a transition matrix and label it T.
MATRICES:   Answer – Q.1 Part C c)  Calculate the number of employed and unemployed people in the second year. Label the answer as A2. To find these numbers, you will have to multiply the number of people in each category to each column in the transition matrix.  1640  x   0.9   =   1476 160  x   0.7   =   112 1476   +   112   =  1588 1640  x  0.1  =  164 160  x  0.2  =  32 164  +  32  =  196 This means  after 1 year  there will be  1588 people employed  and  196 people unemployed .
MATRICES:   Answer – Q.1 Part D d)  Calculate the number of employed and unemployed people in the third year. Label the answer as A3 To find these numbers, you can either  multiply A2 by the transition matrix , or you can  multiply matrix A1 by T² This calculation indicates that  after two years  there will be about  1566 people employed  and  198 people unemployed.
MATRICES:   Answer – Q.1 Part E e)  Compare the answers and discuss the significance of the changes each year. In the first year there are  1588 people employed and 196 people unemployed.  In the second year there are  1566 people employed and 198 people unemployed. This indicates that the changes are becoming less important each year, but the unemployment rates are increasing.

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DEV1

  • 1. DEVELOPING EXPERT VOICES Applied Math 40s 2007 CREATOR: JENNIFER Question 1 : Matrices
  • 2.
  • 3.
  • 4.
  • 5.
  • 6. MATRICES: Answer – Q.1 Part C c) Calculate the number of employed and unemployed people in the second year. Label the answer as A2. To find these numbers, you will have to multiply the number of people in each category to each column in the transition matrix. 1640 x 0.9 = 1476 160 x 0.7 = 112 1476 + 112 = 1588 1640 x 0.1 = 164 160 x 0.2 = 32 164 + 32 = 196 This means after 1 year there will be 1588 people employed and 196 people unemployed .
  • 7. MATRICES: Answer – Q.1 Part D d) Calculate the number of employed and unemployed people in the third year. Label the answer as A3 To find these numbers, you can either multiply A2 by the transition matrix , or you can multiply matrix A1 by T² This calculation indicates that after two years there will be about 1566 people employed and 198 people unemployed.
  • 8. MATRICES: Answer – Q.1 Part E e) Compare the answers and discuss the significance of the changes each year. In the first year there are 1588 people employed and 196 people unemployed. In the second year there are 1566 people employed and 198 people unemployed. This indicates that the changes are becoming less important each year, but the unemployment rates are increasing.