Portfolio Unit 1
Cover letter
The essential question of the small world isn’t it project is how long it will take until the population in the world covers every inch of the available space in our world.
My personal mathematics knowledge has increased over this project. I have learned many of the main focuses in this project that I have learned and grown off of were logs and standard base. The pow’s helped me a lot to understand and improve my knowledge in this topic.
The linear functions, which have the form y=mx+b is a straight line. One assignment, for example, was Find that Base!
In this assignment we were asked to find the base of ax that would give us a proportionality constant of one. This is important because the derivative will equal the y–value. I used 2 and 3 for the base and found the derivative and y–value for one point. Then, I divided the derivative by the y–value. The base of 2 was too small and the base of 3 was to large. I already knew about e, which has a value of 2.718, so I tried it and got a proportionality constant of one. The rate of change is constant for this function and it growth occurs when a quantity grows by different, but proportional amounts. The linear function, also represents the starting points on a line. The initial value is the output value when the input is 0. The function is used for looking at a list of ordered things.
The exponential function, which have the form y=kecx is a curve. One assignment, for example, was Return to Small World, isn’t it?
In this assignment we were tasked to find out what year the population would reach approximately 1.6x1015 people. We had a table with a lot of data. We plugged all data into geogebra. Now, we had a graph, which showed the data plotted. The data appeared logarithmic, so I made an equation in the form y=k•ecx . The rate of change is proportional for this function and it growth occurs when a quantity grows by multiples amounts. The exponential function, also represents starting points on a curve. The initial value is the output. The function is used for the growth of bacteria or for the population growth.
My best approximating function for human population growth is N(t)=N0 • et.
The population reaches 1.6•1015, 3530 years.
The essential question of the small world isn’t it project is how long it will take until the population in the world covers every inch of the available space in our world.
My personal mathematics knowledge has increased over this project. I have learned many of the main focuses in this project that I have learned and grown off of were logs and standard base. The pow’s helped me a lot to understand and improve my knowledge in this topic.
The linear functions, which have the form y=mx+b is a straight line. One assignment, for example, was Find that Base!
In this assignment we were asked to find the base of ax that would give us a proportionality constant of one. This is important because the derivative will equal the y–value. I used 2 and 3 for the base and found the derivative and y–value for one point. Then, I divided the derivative by the y–value. The base of 2 was too small and the base of 3 was to large. I already knew about e, which has a value of 2.718, so I tried it and got a proportionality constant of one. The rate of change is constant for this function and it growth occurs when a quantity grows by different, but proportional amounts. The linear function, also represents the starting points on a line. The initial value is the output value when the input is 0. The function is used for looking at a list of ordered things.
The exponential function, which have the form y=kecx is a curve. One assignment, for example, was Return to Small World, isn’t it?
In this assignment we were tasked to find out what year the population would reach approximately 1.6x1015 people. We had a table with a lot of data. We plugged all data into geogebra. Now, we had a graph, which showed the data plotted. The data appeared logarithmic, so I made an equation in the form y=k•ecx . The rate of change is proportional for this function and it growth occurs when a quantity grows by multiples amounts. The exponential function, also represents starting points on a curve. The initial value is the output. The function is used for the growth of bacteria or for the population growth.
My best approximating function for human population growth is N(t)=N0 • et.
The population reaches 1.6•1015, 3530 years.
Selection of work
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Reflection
I already had this topic in Germany but I learned something about the topic in a different way, which gets me a different understanding about exponents.
I think this topic is kind of important in my life but I don’t really need exponents in my future. Sometimes I was really bored because I already had this topic in Germany. But it was interesting to learn about exponents in a different way or perspective.
I feel that my work was most of the times good but I also had some bad assignments. Sometimes I was really confused because I knew two different ways to calculate exponential and linear functions.
I learned the best with examples and alone, for example with work time. I have grown as a mathematician in this unit because I learned something new about exponents. But most of the time it was confusing to learn one topic in two different methods.
In my personal view it is easier to learn without groups but sometimes it was really helpful and my opinion has changed that group work is bad or not effective for my personal way to learn.
I already had this topic in Germany but I learned something about the topic in a different way, which gets me a different understanding about exponents.
I think this topic is kind of important in my life but I don’t really need exponents in my future. Sometimes I was really bored because I already had this topic in Germany. But it was interesting to learn about exponents in a different way or perspective.
I feel that my work was most of the times good but I also had some bad assignments. Sometimes I was really confused because I knew two different ways to calculate exponential and linear functions.
I learned the best with examples and alone, for example with work time. I have grown as a mathematician in this unit because I learned something new about exponents. But most of the time it was confusing to learn one topic in two different methods.
In my personal view it is easier to learn without groups but sometimes it was really helpful and my opinion has changed that group work is bad or not effective for my personal way to learn.