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Unit - Exponential Function: Real World Applications

Grade Level - High School Algebra II

Goals -
1) Students will understand how to calculate compound interest.

2) Students will explore the impact of differences in income on long term economics.

3) Students will explore the effects of of wage discrimination.

Lesson Explanation: In this lesson students will learn about wage discrimination and apply what they have learned regarding exponential functions to explore the long term implications of wage gaps.

Additional Note:
As I was researching the topic of unequal pay I was constantly looking out for any articles that might address the long term impacts of unequal pay while considering expenditures and/or interest earned/paid on surpluses/deficits.  I was however unable to find any such studies in spite of several explicit searches.  I'm not sure whether this is due to the nature of my queries, the difficulties involved in calculating such information, or simply a lack of studies on this topic.

Standard - CC.1.2.9-10.L

Read and comprehend literary non-fiction and informational text on grade level, reading independently and proficiently.

The articles provided are all examples of non-fiction, informational text.

Standard - CC.1.3.9-10.B

Cite strong and thorough textual evidence to support analysis of what the text says explicitly as well as inferences and conclusions based on an author’s explicit assumptions and beliefs about a subject.

This unit would be a great opportunity to have students read up on equal pay issues and have an informed and respectful classroom discussion.  The best form of this discussion will include explicit textual evidence.

Standard - CC.1.4.9-10.I

Distinguish the claim(s) from alternate or opposing claims; develop claim(s) fairly, supplying evidence for each while pointing out the strengths and limitations of both in a manner that anticipates the audience’s knowledge level and concerns.

The aforementioned discussion directly addresses this standard as well.

Standard - CC.1.5.9-10.D

Present information, findings, and supporting evidence clearly, concisely, and logically such that listeners can follow the line of reasoning; ensure that the presentation is appropriate to purpose, audience, and task.

Again a discussion or even short individual presentations on this issue match this objective.

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Standard - CC.2.1.HS.F.1
Apply and extend the properties of exponents to solve problems with rational exponents

Standard - CC.2.2.HS.C.5
Construct and compare linear, quadratic and exponential models to solve problems.

Standard - CC.2.2.HS.C.6
Interpret functions in terms of the situation they model.

-Equal pay doesn't start out as an exponential problem.  Month by month it's a linear problem with consistent additions and subtractions of steady amounts of cash based on income and expenses.  However when students are pushed to consider what will happen with surpluses and deficits they will quickly find themselves in the exponential worlds of interest, investment, and debt.
-This topic provides many avenues to explore the real world implications of exponential functions and to establish how they differ from linear functions.

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The Equal Pay Act of 1963 required employers to give equal pay for equal work. This law came about in no small part due to the large numbers of women who worked in factories during World War II. However, despite attempts to pass an anti-wage discrimination law, such as the Women's Equal Pay Act of 1945 which failed to pass, no significant progress had been made on the subject of equal pay. In 1960 women still earned less than two thirds of what men did for their work. However, in spite of the Equal Pay Act, and several laws that followed it, in 2016 women were earning just 82 cents to the dollar according to the Bureau of Labor Statistics.

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Equal Pay Act - Facts & Summary - HISTORY.com

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Find out more about the history of Equal Pay Act, including videos, interesting articles, pictures, historical features and more. Get all the facts on HISTORY.com

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According to Blau and Kahn (2016) in 2010 on average a woman would earn 82.1% of what a man would earn working the same job with the same education, experience, race/ethnicity, and living in the same region and metropolitan area.  According to the same study women earned only 71.1% of what men did in 1980, but by 1989 pay had reached levels similar to those of 2010. The National Women's Law Center translated these pay differences into years of work. That is how many years of work would it take for a woman to earn as much as a man would earn over 40 years of work. The numbers are quite shocking, but the reality is likely worse because the NWLC fact sheet doesn't take into account expenditures or investments of any kind.

Blau, Francine D.; Kahn, Lawrence M. (2016). The Gender Wage Gap: Extent, Trends, and Explanations, IZA Discussion Papers, No. 9656, Institute for the Study of Labor (IZA), Bonn

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Here's a poem written by a 14 year old on the subject of equal pay. The information that it presents is similar to the other sources, but we're in the business of education it's practically in our job description to repeat ourselves. This is also the potential starting point to give students the opportunity to generate their own poems or other media on the subject of equal pay.

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Right now, women face a wage gap in every single state. For those of you who don't know what that means it's simple: women are paid on average 79 cents on the dollar for doing the same job as a man. And the wage gap isn't a symptom of women being less educated. Women with doctoral degrees are paid less than men with master's degrees, and women with master's degrees are paid less than men with bachelor's degrees.

But the wage gap doesn't just exist across gender. The racial wage gap in America has not changed in thirty five years. New data from the Pew Research Center analysis of Bureau of Labor Statistics cites that black men earned 73% of white men's hourly earnings in 2015 - the exact percentage they earned in 1980. So how do we fix this?

Well luckily we can turn to the wisdom of a 14-year-old. That's right, Owen Pallenberg wrote another poem for us. This time the incredible young man is left to wonder why we're not doing anything about the wage gap in America.

When we asked Owen why he wrote the poem he said, "I decided to write about the issue of the gender and race Wage Gap in our country because it is a very serious problem that has been recently overlooked due to the issues with President Trump, Syria, Health Care, and in honor of Mother's Day and the first annual 50/50 day."

Presented in full. We give you "79 Cents" by Owen Pallenberg:

A woman makes on average 79 cents to the man's buck,

So the woman makes less because of her chromosome's luck.

This problem in our nation needs to end,

Because yes, a woman makes less...I know it's hard to comprehend.

Minimum wage in California is $10.50 for a man,

More like $8.92 for a woman, making it hard to create a viable financial plan.

People claim that this gap is just a myth,

But it's a proven fact that they're losing out on more than one fifth.

The gap just gets worse for married women, women of color, and even mothers,

Ridiculous, I know. Shouldn't we all get paid the same as one another?

Why are women blamed for things they can't control,

Once men and women are equal, we will finally reach our ultimate goal.

Just take a look at the US Women's National Soccer Team,

They earn about 25% of what the men make, which is really quite extreme,

Even though the women generate more revenue and won the World Cup,

They get paid much less to lace them up.

Black women make 63 cents to the man's buck,

And Latina women earn only 54 cents, so I guess they're just out of luck.

Deniers of these stats are obviously citing the alternative facts,

Because it is quite clear that women receive a sales, property, income, and "woman" tax.

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This 14-Year-Old's Poem Breaks Apart The Wage Gap

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Right now, women face a wage gap in every single state. For those of you who don't know what that means it's simple: women are paid on average 79 cents on the dollar for doing the same job as a man. And the wage gap isn't a symptom of women being less educated.

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This song is from the Pajama Game, a musical which my high school preformed during my senior year.  The musical tells the story of a labor dispute between a company and its employees' union over pay.  In this number the workers talk about what the small pay increase (7 1/2 cents) that they are asking for will impact them over the years. It's also an ear-worm so the students should at the very least remember this song when finals come round

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The Pajama Game - 71/2 Cents (Seven and a Half Cents)

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First of all it is obviously better to be paid more.  If you had a choice of working for $18/hour or for $20/hour in the same job (that's 80%), you wouldn't have think before picking the higher wage.  But what does that $2/hour difference really amount to?

-In one forty hour work week that's $80 dollars.
-In  one year that's around $4,000.

While these are relatively small amounts of money they make a difference.  If two people spend the same amount of money in a year the person who earns $2/hour more has an extra $4,000 dollars saved away in a bank account, or invested.

Questions -
1. If you were working and suddenly started to earn $80 more each week, how would you use that money?

2. Using the compound interest formula (see below) how much would the $4,000 extra the man earned be worth if he immediately invested the full amount into an account earning 0.8% annual interest compounded quarterly and left it there for 10 years? 20 years? 30 years? <$4332, $4693, $5083>