Part 1: Unit Summary Learning Statement The start of this math semester has brought many challenges and learning opportunities my way. Understanding different functions was sometimes hard for me, but I found that once I was able to get a grip and understand one, the others proved to be simple as well. In the beginning I struggled with the exponential growth and decay unit, having to reach out and get help from friends. Once I got a better understanding of this, I felt confident moving onto the next unit, which was Compounding Interest. I feel like I was really ready for this one and got a lot of real world information out of it. Moving into the next few units with more knowledge, I was able to grow in my math ability and learn new things that I’ll use in the future. Through class discussions where everyone had to go up to the board, I washed pushed out of my math abilities comfort zone and learned things on my own to share with the class. Logarithm assignments also helped me put everything I’d learned together to solve for a final answer. By using the Habit of a Mathematician “collaborate and listen,” I was able to understand this math and work with others.
Applying and using exponential growth and decay
Describe how you made sense of the exponential formy=abx
I made sense of this topic by plugging in the exponents to the setup of this function. The exponent form is an outline of the function needed to solve whatever problem, so by replacing the numbers given I learned to solve it.
Describe how you made sense of growth and decay rate
b = 1 + r
b = 1 -r
Since exponential growth is the rapid increase of growth in a problem, and exponential decay is the decrease of the problem, I plugged this function in to get an answer.
Compounding interest
Describe how you made sense of compounding interest and simple interest?
I feel like I connected with this unit more than the others. It was fun for me and not as challenging as some of the other functions. I made sense of it by paying attention and setting the different aspects apart to figure them out before putting them together to solve
Describe how you made sense of compounding interest and continuously compounding interest?
Compounding Interest is the addition of interest (upon interest.) It’s the sum that’s added to a deposit that’s already in the bank, so when the money is taken out, that and the previous interest are earned. Continuously compounding interest is the interest principle continually earning more interest itself. By knowing this, I was able to set up a function for problems with these factors and accurately solve it.
Describe howe(Euler’s Number) can be found using the following formula(1 + 1n)n (Hint: Start with n = 1 and keep getting bigger 10, 100, 1000, etc) What is happening as n gets bigger? *
e is a special number that occurs often in nature and science as well as continuously compounding interest situations. An irrational number represented by the letter e, the equal ion ends up being A=PErt P being the principle, R the rate, and T the time. By plugging in this function, you can solve for the problem above.
Solving for exponents in equations
Describe how you made sense of solving for exponents in equations when the bases can be made the same.
I made sense of solving for exponents in equations where the bases were the same by taking the log from both sides and using that to solve for the variable.
Describe how you made sense of solving for exponents in equations when the bases are not the same.
When exponents in equations don’t have the same base, I learned to rewrite the problem using the same base. Once the bases are the same, you can get rid of them and move on to making the exponents equal to each other as well. Once simplified, you can solve.
Logarithms
Describe how you made sense of converting between the logarithmic and exponential form of an equation.
I made sense of converting the logarithmic and exponential forms of an equation by knowing that a log is an inverse function of an exponential function, and if there’s an exponential function (such as Y=b*) then the log function (to the base b) can be used to obtain X.
Describe how you made sense of the Log Properties.
I made sense of log properties by separating the different properties, and setting the base a on the left, the properties on the right, and then solving