Answered: Population of the United States 170-… | bartleby

College Algebra (MindTap Course List)

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter8: Sequences, Series, And Probability

Section8.7: Probability

Problem 54E: Conditional probability If 40 of the population have completed college, and 85 of college graduates...

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Question

The bar graph shows the population of the United States, in millions, for seven selected years. There are two functions that model the data (see attached), Solve,

a. Write a function that models the total U.S. population, P(x), in millions, x years after 1985.

b. Write a rational function that models the fraction of men in the U.S. population, R(x), x years after 1985.

c. What is the equation of the horizontal asymptote associated with the function in part (b)? Round to two decimal places. What does this mean about the percentage of men in the U.S. population over time?

Population of the United States
170-
Male
162
157 157
Female
160
151 152
147
143
138
150
140
134
130
127 129
122 121
120-116
110
100
1985 1990 1995
2000
2005 2010 2014
Year
Population (millions)

Here are two functions that model the data:
M(x) = 1.48x + 115.1-
Male U.S. population, M(x), in millions,
x years after 1985
Female U.S. population, F(x), in millions,
x years after 1985
F(x) = 1.44x + 120.9.-

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Tax Table Here are selected entries from the 2014 tax table that show the federal income tax owed by those married and filing jointly. The taxable income and the tax are both in dollars. Taxable income Tax 72, 000 9896 72, 200 9926 72, 400 9956 72, 600 9986 72, 800 10, 016 73, 000 10, 046 73, 200 10, 076 73, 400 10, 106 73, 600 10, 136 73, 800 10, 169 74, 000 10, 219 74, 200 10, 269 Over what two parts of this table is the tax a linear function of the taxable income? Find formulas for both linear functions, and explain in practical terms what the slopes mean.
Conditional probability If 40 of the population have completed college, and 85 of college graduates are registered to vote, what percent of the population are both college graduates and registered voters?
Population Genetics In the study of population genetics, an important measure of inbreeding is the proportion of homozygous genotypesthat is, instances in which the two alleles carried at a particular site on an individuals chromosomes are both the same. For population in which blood-related individual mate, them is a higher than expected frequency of homozygous individuals. Examples of such populations include endangered or rare species, selectively bred breeds, and isolated populations. in general. the frequency of homozygous children from mating of blood-related parents is greater than that for children from unrelated parents Measured over a large number of generations, the proportion of heterozygous genotypesthat is, nonhomozygous genotypeschanges by a constant factor 1 from generation to generation. The factor 1 is a number between 0 and 1. If 1=0.75, for example then the proportion of heterozygous individuals in the population decreases by 25 in each generation In this case, after 10 generations, the proportion of heterozygous individuals in the population decreases by 94.37, since 0.7510=0.0563, or 5.63. In other words, 94.37 of the population is homozygous. For specific types of matings, the proportion of heterozygous genotypes can be related to that of previous generations and is found from an equation. For mating between siblings 1 can be determined as the largest value of for which 2=12+14. This equation comes from carefully accounting for the genotypes for the present generation the 2 term in terms of those previous two generations represented by for the parents generation and by the constant term of the grandparents generation. a Find both solutions to the quadratic equation above and identify which is 1 use a horizontal span of 1 to 1 in this exercise and the following exercise. b After 5 generations, what proportion of the population will be homozygous? c After 20 generations, what proportion of the population will be homozygous?

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