According to the Bureau of Labor and Statistics, in 2022 “Average expenditures per consumer

unit for 2022 were $70,021,” where “consumer units include families, single persons living

alone or sharing a household with others but who are financially independent, or two or more

persons living together who share expenses.”

a. “The average American lives on $𝐷𝐷 per day” is a common type of statistic used (not just

about Americans either). Using the information above, determine a reasonable amount

that could represent 𝐷𝐷 in this statistic. Be sure to explain your reasoning.

b. Using your average dollar amount per day for an American, for how many days could an

American live on one trillion dollars? How many years is that? Decades? Centuries?

Millennium?

c. The average life expectancy of an American in 2015 was about 79 years

(data.worldbank.org). With this in mind, about how many Americans could live their

whole lives on one trillion dollars?

### Part (a): Determining Daily Expenditure $ D $

The total average expenditures per consumer unit in 2022 were given as $70,021 annually. To convert this to a daily average expenditure $ D $, we divide the annual amount by the number of days in a year:

\[
D = \frac{70,021}{365} \approx 191.84
\]

Thus, the average American lives on approximately **$191.84 per day**. 

**Reasoning**: This value reflects daily spending based on the average yearly expenditure data provided by the Bureau of Labor and Statistics. Since we are concerned with daily costs, dividing the total by 365 days in a year gives us a reasonable estimate for $ D $.

---

### Part (b): Living on One Trillion Dollars

Now, let’s calculate how long an average American could live on **$1 trillion**.

- **One trillion dollars** is $ 1,000,000,000,000 $ dollars.
- We know that the average daily expenditure is $ 191.84 $ dollars.

The number of days an average American could live on one trillion dollars is:

\[
\text{Days} = \frac{1,000,000,000,000}{191.84} \approx 5,212,820,768 \text{ days}
\]

Next, we convert this to years, decades, centuries, and millennia:

- **Years**:
\[
\text{Years} = \frac{5,212,820,768}{365} \approx 14,278,970 \text{ years}
\]
- **Decades**:
\[
\text{Decades} = \frac{14,278,970}{10} \approx 1,427,897 \text{ decades}
\]
- **Centuries**:
\[
\text{Centuries} = \frac{14,278,970}{100} \approx 142,789 \text{ centuries}
\]
- **Millennium**:
\[
\text{Millennium} = \frac{14,278,970}{1000} \approx 14,279 \text{ millennia}
\]

So, one trillion dollars could sustain an American for about **14.3 million years**, or equivalently, **1.43 million decades**, or **142,789 centuries**, or **14,279 millennia**.

---

### Part (c): Number of Americans Who Could Live Their Whole Lives on One Trillion Dollars

We are given that the average life expectancy of an American is **79 years**. To find out how many Americans could live their whole lives on one trillion dollars, we first need to calculate how much an American spends in a lifetime.

- **Lifetime Expenditure**:
\[
\text{Lifetime Expenditure} = 191.84 \times 365 \times 79 = 5,528,732.8 \text{ dollars}
\]

Now, divide the total one trillion dollars by the lifetime expenditure per American:

\[
\text{Number of Americans} = \frac{1,000,000,000,000}{5,528,732.8} \approx 180,899
\]

Thus, approximately **180,899 Americans** could live their entire lives on one trillion dollars, given a life expectancy of 79 years and average daily expenditure of $191.84.

---

### Summary:

- **Daily expenditure $ D $**: $191.84 per day.
- **Days an American could live on $1 trillion**: 5.21 billion days (~14.28 million years).
- **Number of Americans who could live their whole lives on $1 trillion**: 180,899.

Would you like further clarification on any of these points?

---

Here are 5 related questions to explore:

1. How would the daily expenditure $ D $ change if inflation increased yearly expenditures by 3%?
2. If the average expenditure per American increased by 5%, how many fewer Americans could live on one trillion dollars?
3. What would be the daily expenditure for an American living at 50% of the average expenditure rate?
4. How would the results differ if we used a leap year for the calculation instead of 365 days?
5. How much more would an American spend over a 90-year life expectancy instead of 79 years?

**Tip**: Always double-check large unit conversions (like from days to years or decades) to avoid errors in very long-term calculations!

According to the Bureau of Labor and Statistics, in 2022 'Average expenditures per consumer unit for 2022 were $70,021,' where 'consumer units include families, single persons living alone or sharing a household with others but who are financially independent, or two or more persons living together who share expenses.'

a. 'The average American lives on $𝐷𝐷 per day' is a common type of statistic used (not just about Americans either). Using the information above, determine a reasonable amount that could represent 𝐷𝐷 in this statistic. Be sure to explain your reasoning.

b. Using your average dollar amount per day for an American, for how many days could an American live on one trillion dollars? How many years is that? Decades? Centuries? Millennium?

c. The average life expectancy of an American in 2015 was about 79 years (data.worldbank.org). With this in mind, about how many Americans could live their whole lives on one trillion dollars?

Explore how to calculate the average daily expenditure for Americans based on the 2022 data from the Bureau of Labor and Statistics, determine how many days an American could live on one trillion dollars, and estimate how many Americans could live their entire lives on that amount. Includes detailed step-by-step explanations of the mathematical concepts involved.

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