Exponent Rules
When I was introduced to exponent rules in class I very confident in my work since it was just looking at rules that applied to exponents. Then this quickly turned into using multiple exponent rules to solve algebraic expressions that involved exponents. Most of these rules our very simple for example
(2^3)2= (2)(2)(2) x (2)(2)(2) =64 The rule here is (xm)n = x(m)(n)
(2^2)(2^3)= (2)(2)(2)(2)(2)= 32 The rule here is (xm)(xn) = xm+n
2^4/2^2= (2)(2)(2)(2)/(2)(2) = 4 The rule here is xm/xn = xm-n
((2)(2)(2)(2))^0= 1 The rule here is x0 = 1
Overall this math unit was fairly simple and I felt extremely comfortable doing it. A habbit of a mathematician I used for this topic was taking apart and putting back together. Mostly because the whole premises of doing this math is learning how to take apart the equation learning the rules and putting it back together.
Exponential Growth and Decay Models
Exponential Growth and decay models were pretty tricky for me at first since I missed the three days in which we were introduced to this topic but I quickly caught onto the topic. Like the previous this topic wasn’t that hard to evaluate and understand it was more or less memorizing certain rules and looking for keywords or phrases. For example
A rate that is decreasing follows this rule:
P = A(1-r)t
A rate that is increasing follows this rule
P = A(1+r)t
There is also the wording aspect of these problems such a decrease, increase, incline, decline, etc.. Any word that can signify the way a slope could look is a key detail into finding out what equation you are going to be using. What is a rate you might ask well what a great question is what I would respond with. A rate is a percentage of something that is either being taken away or added to a base number or exponent. A habit of a mathematician that I had used for this math concept is looking for patterns. By looking for patterns in the writing or equations it becomes easier to memorize the equations and visualize what the slope of the graph will look like before you even start the problem.
Forms of Exponential Equations
For Forms of exponential equations I came in with a very confident approach since the rest of this math unit was so easy but that was not the case for this section of the unit. Everything about it seemed really similar to the rest of the unit until that dreaded moment. I had realized that this unit used algebra heavily and algebra is one of my weaknesses in math because I find it so tricky. The first problem was a basic equation that we just had to set up and find a certain answer. Then the problem evolves by doubling certain values. Overall this problem was very simple and easy. But the next problem turns up the heat by making us look at everything we learn to solve equations that used variables. For example we had to prove that 5 equations all equaled the same value by using previous exponent rules to find the answers. But the twist was that all the equations used a variable as the time value or t for short. So to solve them you had to either manipulate the equation or put in values for t. Since putting in value for t completely gets rid of the algebra I decided to do that. For this last wrap up section for the unit I decided it would be a good idea to keep my work organized since it required me to use so many exponent rules. If I didn’t stay organized it would become very easy to get lost in my work.
When I was introduced to exponent rules in class I very confident in my work since it was just looking at rules that applied to exponents. Then this quickly turned into using multiple exponent rules to solve algebraic expressions that involved exponents. Most of these rules our very simple for example
(2^3)2= (2)(2)(2) x (2)(2)(2) =64 The rule here is (xm)n = x(m)(n)
(2^2)(2^3)= (2)(2)(2)(2)(2)= 32 The rule here is (xm)(xn) = xm+n
2^4/2^2= (2)(2)(2)(2)/(2)(2) = 4 The rule here is xm/xn = xm-n
((2)(2)(2)(2))^0= 1 The rule here is x0 = 1
Overall this math unit was fairly simple and I felt extremely comfortable doing it. A habbit of a mathematician I used for this topic was taking apart and putting back together. Mostly because the whole premises of doing this math is learning how to take apart the equation learning the rules and putting it back together.
Exponential Growth and Decay Models
Exponential Growth and decay models were pretty tricky for me at first since I missed the three days in which we were introduced to this topic but I quickly caught onto the topic. Like the previous this topic wasn’t that hard to evaluate and understand it was more or less memorizing certain rules and looking for keywords or phrases. For example
A rate that is decreasing follows this rule:
P = A(1-r)t
A rate that is increasing follows this rule
P = A(1+r)t
There is also the wording aspect of these problems such a decrease, increase, incline, decline, etc.. Any word that can signify the way a slope could look is a key detail into finding out what equation you are going to be using. What is a rate you might ask well what a great question is what I would respond with. A rate is a percentage of something that is either being taken away or added to a base number or exponent. A habit of a mathematician that I had used for this math concept is looking for patterns. By looking for patterns in the writing or equations it becomes easier to memorize the equations and visualize what the slope of the graph will look like before you even start the problem.
Forms of Exponential Equations
For Forms of exponential equations I came in with a very confident approach since the rest of this math unit was so easy but that was not the case for this section of the unit. Everything about it seemed really similar to the rest of the unit until that dreaded moment. I had realized that this unit used algebra heavily and algebra is one of my weaknesses in math because I find it so tricky. The first problem was a basic equation that we just had to set up and find a certain answer. Then the problem evolves by doubling certain values. Overall this problem was very simple and easy. But the next problem turns up the heat by making us look at everything we learn to solve equations that used variables. For example we had to prove that 5 equations all equaled the same value by using previous exponent rules to find the answers. But the twist was that all the equations used a variable as the time value or t for short. So to solve them you had to either manipulate the equation or put in values for t. Since putting in value for t completely gets rid of the algebra I decided to do that. For this last wrap up section for the unit I decided it would be a good idea to keep my work organized since it required me to use so many exponent rules. If I didn’t stay organized it would become very easy to get lost in my work.