Math in the News: Issue 81

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The document examines the growth of America in terms of states added to the Union and population increase over time based on census data. It shows that states were steadily added to America from 1787 to 1912, while the population has grown in a non-linear manner from 1790 to 2010, initially driven by new states, growth, and immigration, but now primarily reliant on immigration for increases. Graphs and tables of data on states and population demonstrate America's expansion over the centuries.

Economy & Finance Technology

$Math in the News Issue 81 The Growth of America In this issue we look at census and demographic data for the U.S.$

Throughout most of its history America has grown in size
and population. Let’s first look at how America expanded in
terms of the number of states added to the Union.

This table shows how
America grew through
the increase in the
number of states.
(The first 13 states
are lumped into 1787,
when the Constitution
was ratified.)

Here is the graph of the data in the table. This shows that states
were added to the country in a steady, consistent manner.

This graph takes the same data and displays it cumulatively.

This graph is a scatterplot of the data. As you can see it is a linear
function.

This table shows how
America’s population
has grown from 1790
to the start of this
decade. (Source:
Census Bureau.)

Here is a graph of the data. As you can see the population has
grown in a non-linear manner.

Up until the 1960s, there were three forces at work to grow
the US population: (1) new states, (2) normal population
growth, and (3) immigration. But since the 1960s no new
states have been added.

Since the 1980’s the normal growth of the US population
has been flat to a slight decline. This table shows the net
change based on new births vs. deaths.

One of the biggest drivers of the US population now and
for the foreseeable future is immigration. This chart from
the Census Bureau shows how immigration is set to
overtake the normal growth in population.

The New Frontier in better understanding America’s
growth isn’t Geographic, but Demographic.

The document discusses bubble charts, which display three dimensions of data using circles of varying sizes. Bubble charts can show relationships in social, economic, medical, and scientific data sets with dozens to hundreds of values that differ greatly in magnitude. They represent numbers using the area of circles, making them useful for positive values that can differ by ratios of 100,000 while displaying hundreds of values at once. An example bubble chart is presented showing product numbers on the x-axis, sales amounts on the y-axis, and market share percentages as bubble sizes.

2nd ia Yuta Y

YutaYama

This document investigates population trends in China from 1950 to 2008 using different mathematical functions. It finds that an exponential function initially fits the data from 1950 to 1995 well but does not capture the leveling off of population growth seen in later data. A logistic function proposed by a researcher fits the full data set best, accurately modeling the population as it increased rapidly then began stabilizing in more recent years. The best fitting model will help understand and predict China's future population challenges.

Math ia

tykraichok

An investigation analyzed the relationship between population growth rates and GDP rates in 50 randomly selected countries from 2009 to 2010. Population and GDP data from 2009 and 2010 was collected and used to calculate growth rates for each country. A chi-squared test was performed to determine if there was a statistically significant relationship between population growth and GDP rates at the 5% significance level. The results of the chi-squared test were then compared to critical values to determine if the null hypothesis could be rejected or not.

Math IA

ravikanya

Population growth and increases in carbon dioxide emissions both rose significantly from 1980 to 2009. While a positive correlation exists between the two, statistical analysis shows the relationship is weak. The chi-square test results fail to reject the null hypothesis that population growth and carbon emissions are independent. Therefore, while human activities like energy use that produce carbon emissions rise with growing populations, population growth alone does not sufficiently explain increasing carbon dioxide levels according to this analysis. Other factors must also influence annual carbon emission amounts.

Math Internal Assessment

Janniie

The document summarizes a study that investigated the relationship between height and shoe size in 20 women and 20 men. It found a weak positive correlation, such that taller individuals tended to have larger shoe sizes. However, the relationship varied substantially between individuals. A chi-square test found no definitive relationship, though the idea that taller people generally need larger shoes to maintain balance was supported. Limitations included potential inaccuracies in self-reported height and shoe size data.

Math Statistics IA December 2010

david1dave

- The document analyzes the relationship between the average hours of video games played per school week and the average hours of sleep per school night for 50 high school students. - Statistical analysis showed a weak negative linear correlation between video game time and sleep hours, indicating the variables were mostly independent. However, surveying the entire student population may have strengthened the correlation. - While more video game time tended to equal less sleep, there was high variation in the data, and other factors like homework also impacted students' sleep amounts. So the relationship between video games and sleep was inconclusive based on this study.

Ib math studies internal assessment final draft

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The document analyzes the relationship between SAT scores and family income of test takers worldwide based on data from the College Board in 2007. The author conducts a mathematical investigation including generating scatter plots, calculating the least squares regression line and correlation coefficient, and performing a chi-squared test. The results show a strong positive linear correlation between SAT scores and family income, indicating family income has a significant impact on SAT scores. However, the study has limitations as it only includes those who reported income and may not capture all SAT test takers.

Geometric Construction: Creating a Teardrop Shape

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Constructing a teardrop shape involves drawing three circles of different radii using a compass on graph paper. The teardrop shape is formed by the overlapping circular arcs from a radius 5 circle, another radius 5 circle, and a radius 3 circle. The overlapping arcs are highlighted and isolated by erasing the remaining circular areas to reveal the smooth teardrop curve created by the intersecting arcs.

The document discusses summer blockbuster movies. Some key points: - Summer is the peak movie season due to school being out and families looking for affordable entertainment options. - Blockbusters are big-budget films released in the summer that draw huge audiences and make substantial profits. They typically feature recognizable stars, special effects, and family-friendly content. - Examples of past summer blockbusters that fit this profile are provided. - Data on the budget and earnings of Avatar, a highly successful blockbuster, show it had a budget of $425 million and grossed $760.5 million, resulting in a profit of $335.5 million.

Math in the News Issue 110: Summer Travel

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Math in the News: Issue 107

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This document discusses using mathematical models to represent the thawing of frozen turkeys. It introduces logarithmic functions as a model for thawing curves, as the temperature increases over time in a way similar to the inverse of an exponential cooling curve. The document provides guidelines from the USDA for safely thawing turkeys either in the refrigerator over several days or in a water container over several hours, and shows how to construct a logarithmic model to fit starting and ending temperature points for a turkey thawing in the refrigerator.

Tutorials--Cube Root Functions in Tabular and Graph Form

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Tutorials--Logarithmic Functions in Tabular and Graph Form

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This document contains 120 examples of tutorials that construct function tables and graphs for logarithmic functions in tabular and graph form. The tutorials vary the base of the logarithm (base 10 or base 2), the characteristics of the logarithmic function (values of a, b, c for the function y = log(ax + b) + c), and whether the function has a single logarithm or a scaled logarithm (with coefficient d).

Tutorials--Secant Functions in Tabular and Graph Form

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Tutorials--Cosecant Functions in Tabular and Graph Form

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This document describes 65 tutorials that provide examples of constructing tables and graphs for cosecant functions. Each tutorial examines a cosecant function of the form y = csc(ax + b) or y = a * csc(bx + c) + d with different values for the variables a, b, c, and d. The tutorials demonstrate how changing the values of these variables affects the shape of the cosecant function graph and its table of values.

Tutorials--Tangent Functions in Tabular and Graph Form

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Tutorials--Cosine Functions in Tabular and Graph Form

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This document describes 65 tutorials on constructing tables and graphs for cosine functions of the form y=cos(ax+b). Each tutorial varies the values of a and b to demonstrate different characteristics of the cosine function graphed and tabulated over changing domains. The tutorials cover different positive, negative, and fractional values of a and various phase shifts introduced by changing the value of b.

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The Universal Account Number (UAN) by EPFO centralizes multiple PF accounts, simplifying management for Indian employees. It streamlines PF transfers, withdrawals, and KYC updates, providing transparency and reducing employer dependency. Despite challenges like digital literacy and internet access, UAN is vital for financial empowerment and efficient provident fund management in today's digital age.

Who Is Abhay Bhutada, MD of Poonawalla Fincorp

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Abhay Bhutada, the Managing Director of Poonawalla Fincorp Limited, is an accomplished leader with over 15 years of experience in commercial and retail lending. A Qualified Chartered Accountant, he has been pivotal in leveraging technology to enhance financial services. Starting his career at Bank of India, he later founded TAB Capital Limited and co-founded Poonawalla Finance Private Limited, emphasizing digital lending. Under his leadership, Poonawalla Fincorp achieved a 'AAA' credit rating, integrating acquisitions and emphasizing corporate governance. Actively involved in industry forums and CSR initiatives, Abhay has been recognized with awards like "Young Entrepreneur of India 2017" and "40 under 40 Most Influential Leader for 2020-21." Personally, he values mindfulness, enjoys gardening, yoga, and sees every day as an opportunity for growth and improvement.

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Math in the News: Issue 81

1. Math in the News Issue 81 The Growth of America In this issue we look at census and demographic data for the U.S.

2. Throughout most of its history America has grown in size and population. Let’s first look at how America expanded in terms of the number of states added to the Union.

3. This table shows how America grew through the increase in the number of states. (The first 13 states are lumped into 1787, when the Constitution was ratified.)

4. Here is the graph of the data in the table. This shows that states were added to the country in a steady, consistent manner.

5. This graph takes the same data and displays it cumulatively.

6. This graph is a scatterplot of the data. As you can see it is a linear function.

7. This table shows how America’s population has grown from 1790 to the start of this decade. (Source: Census Bureau.)

8. Here is a graph of the data. As you can see the population has grown in a non-linear manner.

9. Here is a scatterplot of the same data.

10. Up until the 1960s, there were three forces at work to grow the US population: (1) new states, (2) normal population growth, and (3) immigration. But since the 1960s no new states have been added.

11. Since the 1980’s the normal growth of the US population has been flat to a slight decline. This table shows the net change based on new births vs. deaths.

12. One of the biggest drivers of the US population now and for the foreseeable future is immigration. This chart from the Census Bureau shows how immigration is set to overtake the normal growth in population.

13. The New Frontier in better understanding America’s growth isn’t Geographic, but Demographic.

Editor's Notes

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Math in the News: Issue 81

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