Exponents Portfolio (Total points = 12 points)
Audrey Matosian
Exponent Rules
Learning the exponent rules relied pretty heavily on my memory of past lessons on exponents and principles, so going about understanding the rules in a new light was very enlightening for me. For example, being able to use exponents to properly describe more complicated functions like 5x^2 y(2x^4 y^-3)=(10x^6)/y^2, by breaking them down into more comprehensible sections.
It let me use what I already knew to be able to find out how to use exponents on a new level. The gif describes how I felt after the exponent review and we started getting into more complicated terms and functions, leaving me to use whatever I knew about exponents before what I am learning now.
Exponential Growth and Decay Models
I actually really enjoyed learning about exponential growth and decay models, it felt like something I knew how to do efficiently, and it was really fascinating to learn about the applications of functions like e, and what they mean. After learning how the expressions should be set up for monthly, yearly, and continuous compounds, I felt very confident in my ability to comprehend this type of problem. For example, the difference between a monthly or yearly compound, versus a continuous compound.
For compounding interest problems we use:
A=P(1+(r/n))^nt
Wherein
A= amount in the account,
P= the initial deposit (principle)
R= the annual interest rate
N= # of compounds in a year
T= Time of investment in years
However, if the compound is continuous we use:
A=Pe^rt
e is an irrational number used in order to represent a continuous compounding
(this is the population problem)
Also apart of the exponential growth and decay models was this hypothetical scenario of a small country and both its food supply and population increase. Using the same basic principles we learned earlier, we can determine when food supply shortages will or will not occur due to population increase or food supply increase.
Forms of Exponential Equations
This in particular proved to be a major challenge for me, the overall format of the problem wasn’t an issue as much as my confusion was. I do understand the basic concepts of it however, and I am still interested to get more acquainted with these types of expressions. I guess I technically haven’t made sense of this quite yet, but I want to be able to comprehend these forms better.
Audrey Matosian
Exponent Rules
Learning the exponent rules relied pretty heavily on my memory of past lessons on exponents and principles, so going about understanding the rules in a new light was very enlightening for me. For example, being able to use exponents to properly describe more complicated functions like 5x^2 y(2x^4 y^-3)=(10x^6)/y^2, by breaking them down into more comprehensible sections.
It let me use what I already knew to be able to find out how to use exponents on a new level. The gif describes how I felt after the exponent review and we started getting into more complicated terms and functions, leaving me to use whatever I knew about exponents before what I am learning now.
Exponential Growth and Decay Models
I actually really enjoyed learning about exponential growth and decay models, it felt like something I knew how to do efficiently, and it was really fascinating to learn about the applications of functions like e, and what they mean. After learning how the expressions should be set up for monthly, yearly, and continuous compounds, I felt very confident in my ability to comprehend this type of problem. For example, the difference between a monthly or yearly compound, versus a continuous compound.
For compounding interest problems we use:
A=P(1+(r/n))^nt
Wherein
A= amount in the account,
P= the initial deposit (principle)
R= the annual interest rate
N= # of compounds in a year
T= Time of investment in years
However, if the compound is continuous we use:
A=Pe^rt
e is an irrational number used in order to represent a continuous compounding
(this is the population problem)
Also apart of the exponential growth and decay models was this hypothetical scenario of a small country and both its food supply and population increase. Using the same basic principles we learned earlier, we can determine when food supply shortages will or will not occur due to population increase or food supply increase.
Forms of Exponential Equations
This in particular proved to be a major challenge for me, the overall format of the problem wasn’t an issue as much as my confusion was. I do understand the basic concepts of it however, and I am still interested to get more acquainted with these types of expressions. I guess I technically haven’t made sense of this quite yet, but I want to be able to comprehend these forms better.