MAIN TOPIC: EXPONENTIAL FUNCTIONS
Overall Unit Reflection
This unit was particularly challenging for me, especially when it came to understanding word problems, equationa and being able to apply the right formulas to the right questions. At the beginning, I found the material overwhelming, and I often struggled to keep up with the lessons. The concepts didn’t come easily, and I frequently felt frustrated when trying to apply them in assignments and exercises.
However, I also noticed some progress as the unit went on. While I still had trouble with certain topics, I found that I was able to grasp the basics of [a specific concept or skill] better toward the end. I made an effort to ask people around me for help, which helped me gain more confidence in my understanding. Working through practice problems and asking for clarification when needed also helped me solidify my knowledge.
One of the most important things I learned from this unit is the value of persistence. Even when I didn’t understand something right away, I realized that taking my time and breaking down problems step-by-step made a big difference. I also learned that seeking help when I needed it wasn’t a sign of weakness but an important part of the learning process.
Looking forward, I plan to continue reviewing the material more regularly to reinforce my understanding, and I’ll focus on practicing more problems to improve my confidence in applying the concepts. I also want to be more proactive in seeking help earlier, instead of waiting until I feel stuck.
Though in my opinion, this Unit was more of an overview and review for all the things I've learnt in the past, whilst applying my memory skills, solving skills and understanding skills. It contained of simple topics that in my opinion just needed lost of time to practice in order to grasp things - which I still lacked within.
Overall, despite the challenges, I feel that this unit has taught me more than just the course content. It’s helped me develop a more understandable approach to difficult subjects, and I’m confident that with more practice and determination, I’ll continue to improve.
Unit Test Reflection
In the recent unit test, I felt like it was a mix between struggle and the opposite - there were parts that I thought were simple enough to flow through and also parts that conflicted me at times. I now realize that my lack of consistent review and practice directly impacted my performance. I didn’t take enough time to properly go over the material or to do enough practice exercises before the test because of my busy schedule. As a result, I found it difficult to recall important concepts and struggled with applying formulas and methods that I hadn’t fully mastered. Specifically, I had trouble with understanding word problems and applying the right formula to or simply that connecting equations with the right laws in order to be solved, which I now see could have been prevented if I had spent more time reviewing.
This experience has taught me that preparation is key to doing well on any test. I now understand that simply attending class and reading through notes isn’t sufficient for mastering the material. I need to dedicate regular time to review and practice, especially in areas I find more challenging.
I take full responsibility for not managing my time better and failing to prepare adequately. Going forward, I plan to develop a more organized study routine. I will start reviewing the material earlier and allocate specific time for practicing problems. Additionally, I will make use of resources such as using online resources and people around me to help reinforce my understanding of difficult topics.
I’m committed to improving my study habits and ensuring that I am better prepared for the next test. I believe that with more consistent effort and better time management, I will be able to perform much better in future assessments.
Topic Information & Work, Notes
The Law of Indices (or Exponent Rules) refers to a set of mathematical rules that describe how to handle exponents (or powers) when performing operations such as multiplication, division, or raising a power - simplifying calculations by using powers of the same bases.
An exponential function is a mathematical function of the form f(x)=a⋅b^x
a is a constant, often called the initial value.
b is the base, a positive real number
x is the exponent, which can be any real number.
Growth or Decay: If b>1, the function represents exponential growth. If 0<b<1, the function represents exponential decay.
Horizontal Asymptote: The graph approaches a horizontal line (usually y=0) but never touches it.
An exponential equation is an equation in which a variable appears in the exponent. The general form is:
a⋅bx=c
Where:
a is a constant multiplier,
b is the base (a positive real number),
x is the exponent (the variable),
c is a constant.
Exponential functions are widely used in various real-world applications where quantities change at a constant rate. Some key applications include:
Growth/Decay
Compound Interest
Half-lives
Worksheets and Notes
Contact me at parveen.jahangir.18228@wellspringsaigon.edu.vn