Exponents Portfolio
"Tell the story of how you made sense of the different concepts throughout this unit. Be sure to hit all of the following talking points, and include all activities/worksheets that are applicable. Be sure to address a habit of a mathematician and one habit/problem you might have grappled with. You must use artifacts (in class activities and problem sets, notes, class discussions) from this unit as evidence. Find/Create an appropriate meme or animated gif to describe your preparedness with these types of problems."
Exponent Rules
Because I’d done this kind of work before, exponents, or even the expanded rules taught were not of any especial difficulty. However, difficulty aside, the new methods were unknown to me, so learning them had a very large part in the way I understand exponents. A fitting example of this was the case where a number (or variable) would have an exponent represented as a fraction. Previously, I had no idea how one would go about solving such a problem, but after the Henry/Henrietta problem,the solution is more than clear. Another important lesson I learned was (in the same problem) was preferring some orders of operation over others in order to solve a problem quickly and *sometimes* without a calculator.
Here are some rules written below:
2^6 = 64
2^6/2 = √2^6
(10^-4)/(10^-9) = (10^9)/(10^4) = 10^5
2^0 = 1
(2^3)^2 = 2^6
2^4 * 2^8 = 2*12
2^-12 = 1 / 2^12
Because I’d done this kind of work before, exponents, or even the expanded rules taught were not of any especial difficulty. However, difficulty aside, the new methods were unknown to me, so learning them had a very large part in the way I understand exponents. A fitting example of this was the case where a number (or variable) would have an exponent represented as a fraction. Previously, I had no idea how one would go about solving such a problem, but after the Henry/Henrietta problem,the solution is more than clear. Another important lesson I learned was (in the same problem) was preferring some orders of operation over others in order to solve a problem quickly and *sometimes* without a calculator.
Here are some rules written below:
2^6 = 64
2^6/2 = √2^6
(10^-4)/(10^-9) = (10^9)/(10^4) = 10^5
2^0 = 1
(2^3)^2 = 2^6
2^4 * 2^8 = 2*12
2^-12 = 1 / 2^12
Work Evidence For: Exponent Rules
Exponential Growth and Decay Models
Something very helpful in understanding the models used to express exponential equations was the non-continuous equation given to us; p*((1+r)/n)^nt. The time aspect of the equation was pretty straightforward, so I’m mostly impressed with the (1+r) segment. I have remembered this and always will by thinking of this as the equation for a percent, thinking of (1+.04) as 104% rather than 1.04. This made very much sense to me because of my past experience in the stock market, where increases and decreases are measured in the same way. In this series of problems, we also began to delve into the practical uses of these equations, such as modeling the average food consumption of a population and stacking it against the growth of said population. This model can be used to predict the point where Soylent Green becomes popular. ← *Idea for math problem
Work Evidence For: Exponential Growth and Decay Models
Forms of Exponential Equations
These kinds of equations can come in quite the variety of forms, as shown in the Four Physicists problem. This problem was enlightening not only with how much freedom a problem’s form has but also an idea it represented; how a group of people can get different answers whilst all be correct. It also was a hallmark for the idea that the cleanest representation was not always the simplest. For instance, q = 300 (1/2)^t/12 was equal in value to q = 300(.9439)^t. The former was cleaner, more exact, but required more operations to solve. The former, in conjunction with the other 2 equations all would simplify to the latter, it being the simplist. This, however forced us (or, in this case, Mr. Corner) to round our .9439 variable from its non-terminating origin value.