Math OER
Week 4 Homework, Part B

In Oregon, a household's energy usage per month forms a histogram that resembles a bell curve reasonably well for real-life data.

The histogram below shows the monthly electrical useage for a household that has electric heat.

1. In which month does this household use the most electricity?

either January or February
either April or May
either July or August
either October or November

2. Which month has the least deviation from year to year?

April May June July

3. Someone asks, "What is this household's typical monthly electrical usage?" What would make a numeric answer to this question meaningful?

Let's limit the question to a season instead of the entire year
Let's look for a common range of numbers, not a single representative number
Let's discard the 2017 data as obsolete
All of the above

4. When did this family replace their old electric furnace with a modern and more efficient heat pump?

December 1st, 2017 December 1st, 2018 December 1st, 2019

5. The total electrical usage for 2017 was 14,780 kilowatt hours. The total electrical usage for 2019 was 11,513 kilowatt hours. How much less electricity was used in 2019?

272 kilowatt hours 3,267 kilowatt hours

6. Electricity costs an average of 11.3 cents per kilowatt hour. How much less money was spent on electricity in 2019 than in 2017?

$31 $36 $369 $3,067

7. What was the percentage decrease of this household's total annual electricity usage when comparing 2017 to 2019?

22% 28% 78% 128%

8. In this city 80% percent of the electric power is from carbon-free hydroelectric energy, making an overall CO2 emission of 16.2 grams per kilowatt hour. How many kilograms of CO2 did this household's electric use create in 2019?

37 kg 47 kg 187 kg 239 kg

9. A typical gasoline automobile's emission is 8.8 kilograms of CO2 per gallon. This household's car gets 30 miles per gallon. How many miles would they need to drive to the equal CO2 emissions of their annual electricity use?

about 55 miles about 70 miles about 637 miles about 815 miles

10. That household actually drives 10,000 miles per year, which is equivalent to about 333 gallons of gasoline. Find this household's total kg of CO2 emissions for house and car, and then divide by 1,000 to convert kilograms to metric tons. Purchasing a carbon offset costs about $14 per metric ton of CO2. What is the value of the carbon offset cost for this household's house and car?

about $22 about $44 about $223 about $437

Short Answer Question: Let's extend the above line of thought to environmentally responsible investing. Please pardon me as I barf a bunch of information at you.

How much is a typical investor responsible for the carbon emissions created by the companies he or she invests in?

There is no clear answer. The investor does own a share of those companies. But responsibility is also shared with the other people who create, buy, or use the products (food, medicines, computers, travel, cement—a big one!).

To be simple, let's assume that the investor is fully responsible for his or her share of the companies invested in, and only owns an S&P 500 index ETF. What does the math say?

All of the S&P 500 companies together create about 1.85 billion tons of emissions annually, and have a total market capitalization of about 23 trillion dollars.

We can do the division. Someone who owns $1,000 of an S&P 500 index fund is in some sense "owning" 1.85 billion tons ÷ 23 trillion dollars × 1,000 dollars ≈ 0.08 tons of emissions annually.

Prices for carbon offsets have huge variation. At an average price, 0.08 tons of annual carbon emissions costs about $1 of carbon offsets each year. But we might instead use the annual social cost of carbon that experts agree on better at about $50 per ton, which assigns 0.08 tons a social cost of 0.08 × $50 = $4 per year for that $1,000 investment.

So our answer is about $4 annually per $1,000 invested. We could say the responsibility is about four-thousandths of that person's investment worth annually.

By the way, the S&P 500 companies on average spend 4% of their expenses on emissions reductions. Overall, US companies are spending about 6.5 billion dollars annually on emissions reductions. Although the U.S. still has nearly the highest per capita emissions, it does lead the world in reducing emissions.

Maybe we should popularize the idea that the investors should do something, erring on the side of being completely responsible for the shares they own by contributing four-thousandths of their investment worth each year towards the climiate change crisis?

Investors own about 22% of that total market capitalization. So if every investor annually contributed four-thousandths of their investment worth, it would add 23 trillion dollars × 22% × 0.004 ≈ 20 billlion dollars to the above 6.5 billion dollars per year. That could make carbon-dioxide removing technologies economically feasible many years earlier!

Your task is to present this information as attractively and persuasively as you can on a single page, image, or slide. Group work is encouraged! Use your own words, charts, and/or diagrams.