1. A Lorenz curve L describes the income inequality of a group. For each input x
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1. A Lorenz curve L describes the income inequality of a group. For each input x, L(x) is the percentage of wealth controlled by the poorest fraction x of the group. For instance, if L(0.50) 0.40 for some group, then we say that the poorest 50% of the group controls 40% of the group's wealth As of 2012, a good fit of the Lorenz curve for the U.S.A. is L(z) = 1.415a3-0.86x2 + 0.412. (a) Calculate and interpret the value of L(0.80) using the formula giver. (b) Approximate the value of x so that L(z) 0.90 and interpret the answer. c) Why is it important that L(0)-0? Does this approximate formula satisfy that goal? (d) Why is it important that L(1) = 1? Does this approximate formula satisfy that goal? 2. In reference to the University of Oregon athletics program, the Register Guard newspaper stated on June 10, 2014 that "Ticket revenue is largely a function of how many fans can fit in your football stadium." (a) What is the argument in favor of revenue being a function of number of fans? (b) Do you think that this function would be strictly increasing, strictly decreasing, or neither? Explain (c) Would a linear model for this ticket revenue be appropriate? Why or why not? 3. Consider the table giving the 2012 values for M, the number of mathematics majors, and T the total number of students in attendance at a university at the end of their rth year of attendance. (The "oth" year of attendance should be considered a major declaration upon being admitted to the school) 0818,000 (a) Find and interpret the value of M(3) b) How many students in their second year were enrolled at the university? (c) Find and interpret the value of146 7,500 2514,300 3582,100 4371,800 (d) For what value(s) of b is T(b)Explanation / Answer
L = 1.415x^3 - 0.86x^2 + 0.41x
a)
L(0.80) :
1.415*0.8^3 - 0.86*0.8^2 + 0.41*0.8
0.50208
So, the poorest 80% of the group controls 50.208% of the group's wealth
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b)
1.415x^3 - 0.86x^2 + 0.41x = 0.9
x = 0.977
This shows that 97.7% the poorest control 90% of the group's total wealth.
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c)
L(0) = 0 has to be true because 0% of the poorest, as in no people
has to control no wealth.
Yrs, this does satisfy the goal cuz when we put in x = 0, we get L = 0
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d)
L(1) = 1 is important too
This is cuz when x = 1, as in 100% of the poorest, as in all the people
have to control the entire percentage of the wealth dont they?
This has to happen
L(1) = 1.415 - 0.86 + 0.41
We get 0.965 with this formula
This formula does not satisfy the goal
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