Scribe: Mathematical Modeling

Hello! My name is Tim-Math-Y and I will be your scribe for today's AP Calculus class activities.

To start off the class, we watched a video (located on the post below) about internet safety and etiquette. Remember to be careful as to what you post, because once published, it cannot be removed and any one may view it.

After those couple of minutes, we then laid our eyes on the focus of this class: sets of numbers.

1.) X : 1.1, 1.2, 1.3, 1.4, 1.5

2.) f(X) : 6.341, 5.328, 4.335, 3.362, 2.409

3.) g(X) : 7.050, 5.875, 4.896, 4.080, 3.400

4.) h(X) : 6.340, 5.423, 4.506, 3.589, 2.672

Mr. K seperated us into groups to analyze these sets. Then we began take into account the differences between each term in each set to attempt to discover an underlying function.

1.) X : A simple linear function with a common difference of 0.1.

2.) f(X) : A slightly curved function with a declining graph. It included the differences:

---> 1.013, 0.993, 0.973, 0.953 (We then noticed a 'common differences' of the differences of 0.02)

---> 0.02, 0.02, 0.02, 0.02 (Mr. K stated that the number of 'difference sets' represents the 'degree' of the function)

f(x) in this case, is a function with degree 2.

3.) g(X) : A function that displays a declining curve similiar to an exponential function. It included the differences:

---> 1.175, 0.979, 0.816, 0.68 (which by Chris, says are 'arbitrary' which means: 'to be subject to individual will/judgment with no restriction')

4.) h(X) : A declining linear function with a common difference of 0.917.

After finding these characteristics, Mr. K began to guide the class through the calculator processes to set up these graphs and attempt to find out exactly the type of functions these were. The outcomes were produced with % accuracies that were indeed very close to 100%. However, with mathematical modeling, Mr. K states that there should not be a 100% accuracy.

Quickly referencing his most prized teaching object, the 'block of wood' ("the rectangular prismatic shape has multiple indistinct sides upon represent different representations but are all part of the same block of wood") to the different styles of representation and assigning us Exercise 1.3, questions number 2 and all of the odd numbers, the class ended.

And tomorrow's scribe isssss......... hmmmmmm..... CRAIG! yes yes, him! Show us your magic bro.

Have a great night everyone!