The World Turns!
(1/8 credit in math)
Guess what! You're four years old. A rich aunt wants to provide for your future and she gives you two choices (yeah, right,...as if!). And you've only got five minutes to make the choice.
 |
Option 1: She will give you $1000 a year until you are 21 (seventeen years from now)...OR... |
|
She will give you $1 this year, $2 the next year, and so on, doubling the amount each year until you are 21. |
Take a guess! Which one would you do? No math allowed, but turn it in!
Now it's math time. Figure out how much you would have each year to a total at age 21 using both options. Turn in a sheet of paper which shows your answers AND explains how you got them.
Use a sheet of graph paper to chart BOTH plans. Put money on the left, vertical margin, using units of $5,000. Put years on the horizontal margin, starting with year one to seventeen years. Use a straight, solid line to represent option 1 ($1000 a year). Use a curved, dotted line to represent option 2.
Looking at your graph, answer the following questions and turn them in.
1. If your aunt died ten years after she made the deal, how much money would you have using both options?
2. How many years would it be before you had the same amount of money no matter which option you chose?
3. Why did the money in option 2 increase so rapidly after the 14th year?
4. Which option do you guess would represent the line shown if the graph showed the world's population growth between the years 1650 and 2000?
IMPORTANT TO KNOW!!
Option 1, with $1,000 per year, shows a simple, direct relationship between numbers. This is called LINEAR RELATIONSHIP.
Option 2, with the numbers doubling, is a lot more complicated. Complication relationships between numbers like this are called EXPONENTIAL RELATIONSHIP.
The estimated world population in millions from 1650 to 2000 is shown below. Looking at this information, you should be able to tell that this will be an exponential relationship since there's no obvious pattern's growth. Make your own graph of this information putting population figures on the left, vertical margin and years on the horizontal margin. Based upon what you did in the first graph and what you know about lineal and exponential relationships, decide whether the line should be straight or curved.
YEAR WORLD POPULATION (estimated in millions)
1650 500
1700 600
1750 700
1800 900
1850 1300
1900 1700
1950 2500
1976 4000
2000 7000
To understand why world population is now growing so fast, we need to look at some issues. Read the four "family histories" below and answer the questions. It might be helpful to draw a family tree for each one to help you with the math. If you do this, turn it in with your answers to the questions
Family A: A has one child.
|
1. If that child has one child, how many grandchildren does A have? |
|
2. If the grandchild has one child, how many great grand-children does A have? |
FAMILY B: B has two children and each of them have two children.
|
3. How many grandchildren does B have? |
|
4. If each grandchild has two children, how many great-grandchildren does B have? |
FAMILY C: C has three children and each of them have three children.
|
5. How many grandchildren does C have? |
|
6. If each grandchild has three children, how many great-grandchildren does C have? |
FAMILY D: D has four children and each of them have four children.
|
7. How many grandchildren does D have? |
|
8. If each grandchild has four children, how many great-grandchildren does D have? |
TYING IT ALL TOGETHER
The number of children "multiply" each generation. For family B there are twice as many children each generation and for family D there are four times as many. Few families really have the same number of children each generation. But these examples help explain one reason why the world's population has grown rapidly in the last 100 years.
Another reason is that in most areas of the world, people are living longer. Up until 125 years ago, the world's population was increasing slowly. Although the number of births multiplied, many babies did not live and large numbers of children and adults died from diseases. Over the past 150 years, diet, nutrition, and health care have improved. Scientists have discovered cures for many diseases. As a result, the death rate has been declining rapidly. With more people being born and living longer, the result has been a big jump in the world's population.
There are concerns that as the world population increases, there will be shortages of food, water, and the quality of life will be threatened worldwide.
Benchmarks: 182, 183, 184, 185, 186, 187, 188, 189, 192, 193, 200, 201, 204, 220
