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.