Here’s a statement of mathematical certainty…”On October 31, the world population will reach 7 billion people”. Or will it? The Wall Street Journal article, “How Do You Get to 7 Billion People” discusses this topic and the issues associated with population accuracy.

Extra Credit Assignment (worth 5 points on your next learning packet – comments due by the date and time your packets are due) follow the directions below carefully. If directions are not followed exactly, points will not be earned.

ARITHMETIC STUDENTS (MAT082) – Respond to the following in the comments area below:

- Your first name, last initial, and the class you are in (082)
- The linked article talks about some of the issues with accurately counting people. Name one of these issues and why it makes accurate counting difficult.
- What does the article say about why accurate counting is important? Why do we care? List at least one reason and why it is important.

INTRODUCTORY ALGEBRA STUDENTS (MAT092) – Respond to the following in the comments area below:

- Your first name, last initial, and the class you are in (092)
- Using the listed data for the US Population in 1950, 2010, 2050, make a reasonable estimate for our population in 2100. Explain your process carefully.
- How does your estimate compare to what the article says will be the US population in 2100? What might account for the difference?

INTERMEDIATE ALGEBRA STUDENTS (MAT122 or 121) – Respond to the following in the comments area below:

- Your first name, last initial, and the class you are in (122 or 121)
- Use LINEAR regression to write an equation for the population growth of China from 1950 to 2010. Then, use EXPONENTIAL regression to do the same thing. Include your equations here and explain your processes.
- Use your equations above to compute the population of China in 2050 and include those numbers and calculations here. Which of your models is more accurate to the 2050 prediction?
- What might happen to explain the predicted drop in population from 2050 to 2100? Would either model have anticipated this?

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1. KristenV082

2. It is difficult because october 31st is a projected date they hope is 7 billion because it is a symbolic date. They can’t accuratly count that it will be specifically on that date. It could be months before that date or after because they just have an average that 1 billion people will be born in 12 years, but the census is only counted from 2005 giving an inaccurate counting.

3. The article says accurate counting is very hard to do, there is no exact way to count 7 million. They just have an educated guess and hoping it will be on the 31st. The doctor is hoping it will be in a year or so. It depends on peoples relationships and how they interact or how many kids they have in what period of time. We do not know the exact date for sure, it is a guess and we are just hoping it is on that special day.

RobertaF082

1)The UN states it hasn’t been able to use census data after 2005. It has no data for 25% of the worlds people, not all countries take a census.

2)Accurate counting is important. Governments, businesses, and aide groups use it to plan funding and find trouble spots. Accurate counts help to fund special areas. With the count it also collects ages, it will help plan for retirement benefits for the older people.

1. AliW082

2.The lack of calendar clarity makes it difficult to accurately count. The article also says you can never say in any country how many people are living there one a certain day on a certain time, all population numbers are roughly an estimate since not every nation carries out a census.

3. Accurate counting is important because we use the world population to plan programs such as retirement benefits, education/care for everyone, fertility rates, migration, birth rate per country, etc. If we could have an accurate head count planning for our world would become easier and more efficient.

1) MatthewL082

2) Accurate counting is difficult due to Birth Rate, Mortality, and Life expectancy increasing. For anyone of those three reasons the count gets skewed.

3) Accurate counting is important since our schooling funds, grants, scholarships, etc are based on how many are in that area, school, program, and etc. The reasons why we should care are that much more we need these previous numbers to be accurate because if they are overly inflated then we may not receive the amount we are suppose to or deserve. Same goes the other direction in medical care benefits provided by the state and retirement benefits as in social security provided by america and similar things provided by other countries.

1.Brandilyn,K,121

2.LINEAR regression: 13,150,000X+551,000,000

EXPONENTIAL regression: 551,000,000(1.014921735)^X

I used my calculator and made a table under STAT using L1 and L2. I set 1950 to 0 and 2010 to 60 putting in the appropriate output for each year. From that table I used the LinReg and ExpReg keys to find the equations.

3.Input X=100

LINEAR: 13,150,000(100)+551,000,000=1,866,000,000

EXPONENTIAL: 551,000,000(1.014921735)^(100)=2,423,298,539

After calculating the equations I was surprised to see that LINEAR regression gave me the most accurate prediction. I figured that since its a growth in the population that EXPONENTIAL regression would have been a closer prediction.

4.Neither one of the equations estimates the prediction for China in 2100. Both of the equation are showing a rise in the population not a drop that the chart shows. With the growth rate in the ExpReg it shows the population staying on that same growth pattern. I think that the drop in the population for China in 2100 may be due to them choosing the midpoint of a range for fertility rate for each country. I think that China is more strict on the fertility that country has and monitors it more by requiring people to have less kids then other countries. You see that while China’s population in decreasing, other countries are increasing.

1. Susan, K 121

2. Linear Regression: 13,150,000x +551,000,000

Exponential Regression: 551,000,000(1.04921735)^X

STAT info entered under L1 = 0, 60 L2 = 551,000,000, 1,340,000,000

3. X = 100 Number of years

Linear = 13,150,000(100) + 551,000,000 = 1,866,000,000

Exponential = 551,000,000(1.04921735)^(100) = 2,423,298,539

Exponential is more correct. Linear reflects a constant/steady rate of change while Exponential reflects a more accurate rate of change (multiplicative) growth is faster compared to linear.

4. Reasons for a predicted drop in the population: War, external conflict, natural disaster, man made disaster, fertility rate changes, life expectancy changes, migration (Because migrants tend to adopt birthrate patterns of their new country.

Neither model will have predicted this.

1. LaurenMc 122

2. Linear Regression: 13,150,000x +551,000,000

Exponential Regression: 551,000,000(1.04921735)^X

On TI-83, Entered STAT, info entered under L1 = 0, 60

L2 = 551,000,000, 1,340,000,000

3. Input X = 100 years

Linear = 13,150,000(100) + 551,000,000 = 1,866,000,000

Exponential = 551,000,000(1.04921735)^(100) = 2,423,298,539

Exponential is the most accurate. Exponential has a steady multiplicative change while linear is just an addition to each year and not as fast as an exponential growth rate.

4. Drop in the population may be from natural disaster, wars, population control (decreasing the amount of children families are allowed to have), radiation levels from certain things may effect fertility, etc. Neither model will have predicted this.

1. Sarah B. 121

2. Entered 0 & 60 in the L1 column of Stat, 551,000,000 and 1,340,000,000 in L2.

Linear regression equation- 13,150,000X+551,000,000

Exponential regression equation- 551,000,000(1.0149)^X

2. Linear- 13,150,000X+551,000,000= 1,866,000,000

Exponential- 551,000,000(1.0149)^X= 2,418,114,435

The linear model is more accurate compared to the prediction for the 2050 population listed in the article.

4. The only way I can think that they might be able to predict a decline in the population has to do with China’s enforcement of population control in limiting the number of kids everyone can have. I don’t see how anyone can predict that one country will lose people due to war or natural disaster and another one won’t.

Neither model would have predicted this because they are both increasing.

1. Jess M, 121

2. Linear Regression; 13,150,000x+551,000,000

Exponential Regression; 551,000,000(1.04921735)^x

On the T9 calculator, I entered STAT and plugged in the data; On the L1 column I entered 1950 as 0 and 2010 as 60, and plugged in the corresponding populations in the L2 group. I used the LinReg and ExpReg keys to find my equations.

3. Plugging in 100 for X:

Linear; 13,150,000(100)+551,000,000=1,866,000,000

Exponential; 551,000,000(1.014921735)^100=2,423,298,539

The Linear equation gives a more accurate number, according to the article’s prediction.

4. I think the predicted decline in population could be due to China’s strict population control. Neither model predicts a decline, though. I’m not quite sure how the UN came to the conclusion.

1) Saunders, P. 121hybrid

2) Lin Reg: 13,150,000(x) +551,000,000

Exp Reg: 551,000,000(1.05)^x

On TI-83 plus , I entered STAT, info enter L1 = 0, 60

L2 = 551,000,000, 1,340,000,000

3. Input X = 100

Lin= 13,150,000(100) + 551,000,000 = 1,866,000,000, Exp= 551,000,000(1.04921735)^(100) = 2,423,298,539

Exponential is more accurate, because exponential has a regular increasing change while linear is a addition to each year.

4. The drop may be from natural disaster, wars,diseases, population control, and radiation levels from certain things may effect fertility. I really don’t see how it will drop because china is always over populated. Neither model will have predicted this.

More good follow-up on the “7 billion people” idea…

http://www.scientificamerican.com/article.cfm?id=proofiness-and-human-population-milestones