Unit 7❄️ CP Algebra 2

Big ideas: Logarithms😍

A quantity representing the power to which a fixed number (the base) must be raised to produce a given number or the exponent that indicates the power to which a base number is raised to produce a given number.

Logarithms using base 10
Big Idea: Inverses🌴

Inverses are a reciprocal quantity, mathematical expression, geometric figure, etc., that is the result of inversion. Another way to describe an inverse would be something that is the opposite or reverse of something else.

Inverse functions.
Big Idea: Exponentials☄️

By means of or as expressed by a mathematical exponent, and another way to describe exponentials would be a general increase or rise.

Exponential function
New Discoveries🌅

e is an irrational number that is used to solve logarithms and logarithmic equations. e equals 2.71.

Irrational number e
  • This problem is a good way to show how e works through logs.
  • I learned the process of applying e into problems.
  • This was difficult because putting the log in was challenging figuring out where it went.
  • I used some notes to help determine the steps.

Logarithmic equations are very interesting a fun to complete, but it's also great when inequalities get solved with logarithms.

Logarithmic inequalitie
  • I chose this problem because it shows the process and importantes of logs in inequalities.
  • Learned how to put logarithms into inequalities.
  • The part afterward involving graphing was challenging.
  • I looked at graphhung regular inequalities and how it differed from inequalities with logs and graphed.

When using logs, there is a lot of sepecifc properties you have to follow when solving certain equations.

The property of logarithms.
  • This shows easier ways to exponentials.
  • I learned how to change exponential functions into exponential equations.
  • Difficult learning and remembering the property.
  • I would repeat it a lot to learn it faster.

With exponentials, there comes to be certain graphs and specific equations that can be solved.

Exponential function, and exponential equation.
  • This problem shows the difference between a exponential function and equation.
  • I learned the difference between a exponent function, and exponential equation.
  • This was difficult finding the graph to use.
  • I would get help from certain classmates.

In high school it's important to learn things about later in life, and fortunately we learn how to process compound interest rates.

Compound interest solved problem.
  • I chose this problem because it's important to know and understand.
  • I learned the process of interest rates so I can use it later in life.
  • This was difficult because there is a lot of important, specific numbers that need to be correct.
  • I got help from you in the process.

This new discovery is an example of transferring bases from the problem to the other side. Logarithms are also involved in the process.

Transfer of bases
  • This was a great example for this project and explaining another lesson.
  • Learned the process of bases changing and moving to the other side.
  • It was difficult because logarithms being acquired into the problem was difficult.
  • I used great directions from the internet.
Connections❄️

Also in this lesson we paid close attention to the process of exponential growth and exponential decay. We did a project involving these two key vocab terms called "how to survive a zombie attack." Since there is no such thing as a zombie this is technically wrong, but this paper would work if instead of zombies it was an epidemic of a disease.

Exponential growth and decay
  • I chose this because exponential growth, and decay is important to know later in life. It involves many important factors of our lives like finance.
  • I learned how to calculate long term effects of big numbers involving important events, and also how to graph hit.
  • This is connected through exponential growth, and exponential decay in a certain event or outbreak.
  • This could occur in the future because there is a possible chance that there will be some kind of epidemic involving diseases.
The Future
  • I think logarithms are important to understand in life. They are involved in many jobs, and things we need to know in life.
  • There is many things to still learn about logarithms; like how logs are inputed into calculus? That would be interesting to learn, and a good source to know in life.
  • People underestimate the true Big Idea of math. They don't comprehend how math is everything, and everywhere. Math is needed later in life for so many different important things.
"Pure mathematics is, in its way, the poetry of logical ideas."

https://www.brainyquote.com/quotes/quotes/a/alberteins106697.html?src=t_mathematics

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