Canada, Germany, New Zealand, and Japan

For this homework assignement, I decided to do New Zealand as the fourth country as well because I started doing it in class, eventhought I was not supposed to. Below I have calculated for Canada, Germany, New Zealand, and Japan.

Canada: We are looking for the Death rate!
P(2012) = P(2011) + P(2011) (B - D)
34108860 = 34030590 +  34030590  (0.01028 - D)
- 34030590
78270 = 34030590 (0.01028 - D) Use distributive property here!
78270 = 349834.5 - 34030590D
-349834.5
-271564.5    =  -34030590D
-34030590   = -34030590
Since both the denominator and numerator are negative, we can transform them to be positive, which will give us the same result because a negative divided by a negative is positive, and positive divided by positive is positive.
D = 0.00798

Germany: We are looking for the population in 2012!
P(2012) = P(2011) + P(2011) (B - D)
P(2012) = 81471830 + 81471880 (0.0083 - 0.01097)
Since we have both Birth and Death rate, we can immediately subtract them, and move on to the distributive property.
P(2012) = 81471830 - 217529.8
P(2012) = 81254300

New Zealand: We are looking for the birth rate!
P(2012) = P(2011) + P(2011) (B - D)
4045249 = 4027947 + 4027947 (B - 0.00715)
-4027947  
17302 = 4027947B
+28799.8
46101.8  =   4027947B      
4027947 =   4027947   
B = 0.01144

Japan: We are looking for the death rate!
P(2012) = P(2011) + P(2011) (B - D)
126124097 = 126475700 + 126475700 (0.00731 - D)
126124097 = 126475700 + 924537.4 - 126475700D
126124097 = 127400237.4 - 126475700D
-127400237.4
-1276140.4 = -126475700D
-126475700= -126475700
D = 0.0101

Total World Population

From the graph above, we can see a huge difference between the number of people in the developed and in the developing countries. As we can see starting from the 1930s, the number of people in both regions start to increase, but the slope in the developing region is much steeper. This leads to a bigger increase in the population of the developing region than in the developed one. This is because we have much bigger birth rates than death rates in the developing countries. But we can also see that as we get closer to 2100, the populatin in both countries are not increasing anymore. (Will the planet become too small for all of us? I'm starting to get worried.

Births, Deaths, and Algebra

                                                 

                              Births, Deaths, and Algebra

 Something you need to know:

19.5 births/1000 (1000= be careful! Not /100)
P=Population
P(2012) = P(2011) + P(2011) (B-D)
P(2012)= Want to estimate population for 2012
P(2011) = This is the population we started within 2011
P(2011) (B-D) = This is the growth for 2011
B = Birth rate in decimal form
D = Death rate in decimal form

Macedonia:
Birth Rate: 11.9/1000 = 0.0119
Death Rate: 8.9/1000 = 0.0089
The Equation:
P(2012) = P(2011) + P(2011) (B-D)
P(2012) = 2,114,550 + 2,114,550 (0.0119 - 0.0089)
0.0119 - 0.0089 = 0.003
2,114,550 + 2,114,550 times 0.003
Here, I made a mistake, and my solution at the end was wrong. I first added 2,114,550 + 2,114,550 and then multiplied 0.003! Everybody should watch out at this stage. What I then figured out is that I have to use PEMDAS (Parantheses, Exponents, Multiplication, Divisoin, Addition, Subtraction) in order! This is called the order of operations!
The final result is: 2,120,893.65
To simplify this, the final, FINAL result is 2,120,894. This is the population for the people in 2012.

Future Macedonia:

What will be the population in Macedonia in 2013, 2014, 2015, and 2016? How will we find this out?

Birth Rate: For calculating the average birth rate, I've used values from 2005 - 2011 and I have calculated that the average birth rates are decreased by 0.022 every year!
I got that estimated values of the birth rate is as following:

2011:	2012:	2013:	2014:	2015:	2016:
11.87	11.85	11.63	11.61	11.58	11.56

Death Rate: For calculating the average death Rate I did the same thing, but including different numbers:

2011:	2012:	2013:	2014:	2015:	2016:
8.90	8.928	8.956	8.984	9.012	9.04

I found that the average increase from year to year will be 0.028

Finally I chose to use these values to calculate the estimated values for the Macedonian population:

P(2013) = 2,120,894 + 2,120,894 (11.848 - 8.928 / 1,000)
= 2,120,894 + 2,120,894 times 0.00292
= 2,120,894 + 6193.27 = 2,127,087

P(2014) = 2,127,087 + 2,127,087 (11.61-8.984/1000)
= 2,127,087 + 2,127,087 times 0.002626
= 2,127,087 + 5585.7 = 2,132,672

P(2015) = 2,132,672 + 2,132,672 (11.58 - 9.012 / 1,000)
= 2,132,672 + 2,132,672 times 0.002568
= 2,132,672 + 5,47.7 = 2,138,148

P(2016) = 2,138,148 + 2,138,148 (11.56 – 9.04 / 1,000)
=  2,138,148 + 2,138,148 times 0.00252
= 2,138,148 + 5388 = 2,143,536
Now that I know the formula for each year, I can find out what the population for Macedonia will be even in 2050! It would just be a little tedious though, or I can use a graph to do my estimation easily.

Optional Homework

                                                                 Slopes and Graphs!

Problem # 1:

My Work for problem # 1:

Problem # 2:

My Work for Problem # 2:

Problem # 3:

My Work for Problem # 3:

Life Expectancy

Answers to Questions:

• In words, describe what the graph results mean for your country?

The Graph results mean that each year the population increases by 0.179 years. So we have a positive increase of life age of people in Macedonia.

• How do the life expectancy results relate to the population growth of your country? (Were they what you expected?)

In population growth we also had a positive slope, which means that we have a constant increase in the number of people year by year.

• Can you explain any possible reasons for this relationship?

There are a lot of factors that affect both life expectancy and population growth such as: Life conditions, good medical treatment, a lot of newborn babies, economical issues, etc. If everything previously said is positive, we will have a positive increase in life expectancy and there will be more newborn babies than dead people. This can lead to the positive increase in population growth and that can be observed from the previous graph that I posted in my last blogpost.

Population Growth

The graph below represents the growth of population in Macedonia that I drew using MSExcel.
The formula for calculating the population was:

A = P (1 + r) to the power of n.
Where A =
           P = Population
           r = rate of increase (as a decimal, not percent)
           n = number of years

I have used this formula to calculate how big the population will be in each year starting from 1, and ending to 10, and then I drew a graph.

We can use this graph to predict what the population will be in specific years.

Slope = change in y

             change in x

I drew the pictures above by hand because I was unable to insert a picture from the internet on Geogebra.com

Below I have some information that might be useful.

To begin with, I wrote an equation.

y = w times x + b

If b = 0 we have y = w times x

w = slope

y = height of building

x = length of the shadow

So, we can write our equation as y = -0.875 times x and we can use it for calculating any shadows or building heights.

For example, shadow = 20 m

y = 20 times 0.875 = 17.5 m

Because the sun is moving, this wouldn't be an everyday logical situation. :)

Motions and Functions

                                                        M O T I O N S  &  F U N C T I O N S

                                                                          x = Time (t)
                                                               y = Position of the vehicle
                                     It's important to know that physically time CANNOT be negative!

1) The Explanation of the Motion in each vehicle:

 Vehicle A: y = 30t (red line). It's a straight line that starts from a negative value which passes through 0 and increases fast.

Vehicle B: y = -25x + 1200. It's also a straight line that passes through the y axis at this point: 1200, and then decreases. After 48 seconds it stops.

Vehicle C: y = 0.5x squared. It's an exponential line that is always positive (for every value of x). He first decreases, and then increases after x > 0

                                                                  Answers to Questions:

1) Did all the vehicles depart from the same place? 

No they didn't, some of them have started from the negative side, although we shouldn't count the negative time, because time can't be negative, as I said previously. I think that the same conclusion can be taken for the distance. I also think that a and c are starting from the same position.

 2) Were all of them at the same speed?
                                                                 Speed = Change in Distance

                                                                                 Change in Time

They don't have the same speed. In the first couple of seconds the speed of the vehicle a is the biggest, but after it changes.

3) Were all the speeds constant?

First I thought that vehicle A and B will have a constant speed, but vehicle A will increase its distance while vehicle B will drop its distance to 0, that means that it will certainly slow down, so that B cannot have a constant speed. My answer is that only the speed of A will be constant. 

Homework

                                                           Family Compound Interest Activity

I have completed my homework assignment which is on Moodlic for week 4: Discussing compound interest with your family. My parents have reminded me about one situation (a real life situation) that I didn't know I could apply math in it. This is my situation: When I was born my grandparents have given me 1000 euros and my parents have put it in the bank, it stays there for 16 years. So, I can use that money for whatever I want- A TRIP TO AMERICA was my first choice. This was a great opportunity to calculate how much money I will have in two years!

A = 1000 ( 1 + 0.06 ) ^16 = 2540.4 EUROS

I believe that this is enough money in order to have an awesome trip in America! :)

Homework

What will be the year to year, Personal CPI of this student (or in other words, what will be the percentage increase over the year)?

 Does the answer make sense to you? Should it be this small?

 Look carefully at the table. Does it fairly represent a typical week in the life of an ISB student? What can we do to fix this table? HINT: think about how much popcorn, ice cream and t-shirts you would buy and how many iPads you would buy.

The CPI for our example is too small because we have a price percentage increase (or decrease which is the Ipad in this case) more than 10%. Our CPI should be much bigger.

Our table doesn’t represent a typical year in the life of an ISB student because perhaps students would buy only ONE Ipad or bike, but certainly more than one t – shirt or popcorn bags with popcorn inside.

Homework

September, 19th 2011

Two Real Life Situations:

1) You and your friend decided to go to a huge store called Target, because everything is 70% off. Your friend wishes to buy a very bright and pink shirt, which costs $60. How much money does she need to pay?

Answer:70% of 60 = 42. $42 is the discount. $60 - 42 (discount) = 18 dollars. So, your friend will buy the shirt for $18 instead of $60.

2) My family and I went to a restaurant and ate lunch. When we were finished, my father asked for the bill, and the waiter brought it. The price was $150. Since the waiter was so polite, we decided to give him a tip of 10%. How much money did we give in total?

Answer: 10% of $150 = 15. So, in total we gave $165.

Homework

                                How do you feel about Fractions, Decimals Percents?

Fractions,Decimals + Percentages are quite easy when you have a lot of practice. Ifeel like I have forgotten a lot about this, because I haven’t do it for wholesummer, but when I started doing some problems and catching up with the class,I started to realize that it is not that hard. The hardest part of this isturning Fractions into decimals; because this stage is when you make a lot ofmistakes. For example, I decided to make my own problem, and I made thestupidest mistake when simplifying 14/5. I put 15/5, so the whole problem was amistake. The next stage is easier because all you have to do is use the DUPE toturn the decimal into a percent.