6/26/17- Day 6


60: 5, 7, 9, 13, 23

68: 3, 5, 17, 33

97: 23, 27, 29, 30

179: 3-9 ODD

222: 9, 11, 21-25 ODD

Sections covered: 2.3, 2.4, 2.7, 3.9, 4.4

In Student Journal: p. 34 ALL, p. 35 a-d (write an equation for each as well)

p. 38: 5-7 (use desmos- see this for how to do it: http://support.desmos.com/hc/en-us/articles/202532159-Regressions)

p. 39: #1 a-c, p. 40: 5 (use elimination on two equations to get rid of one variable, then use another combination to get another equation in the same variables, then you should be able to work through your two equations in two variables! After you know one variable, use it to solve for what’s left, and keep working backwards!)

p. 42: 3, 6, 10

p. 54: #2 (bottom of the page) calculate the differences between outputs on the table- notice, it’s not constant like a linear function, the differences are changing. Now calculate the differences between the differencesThey are constant. When first differences are all equal, the function is linear, when second differences are constant, the function is quadratic. Use desmos to model the function (y1˜ax1^2+bx1+c) below a table of the x1, y1 values. To get to the ˜ symbol, go “funcs” then “stats”, and you should see it on the bottom right.

Notice: “a”, the coefficient of x^2 that it gives, is half of your second difference!

p. 58: 9-12 (calculate first and second differences to answer each question and help develop a formula. Note, the “divide second difference by two” only works when your inputs are increasing by one number at a time). If you know a, b, or c, great! If you can’t find one, two, or all three of them, plug in examples of x and y to create a number of equations that can be used to find what’s missing. If only one value is unknown, you only need one (x, y) example to figure it out. For two unknowns, you will need two equations. For three unknowns, you will need 3 equations (this is why we did systems of equations today!).

p. 104: #5, 6- use first, second, and third differences to determine the degree of the polynomial that will best model this function. For #6, you will see that a the level of third differences, you get a constant difference of +18. This tells you that a third degree polynomial can model the data. So you go to desmos, put the data in a table, and underneath that make a function y1 ˜ ax1^3+bx1^2+cx1+d, and desmos will tell you what values of a, b, c, and d make the function fit the data, and also give you an corellation-coefficient (r or r^2) that tells you how will the fit is (r close to 1 or -1 is a good fit, close to 0 is a weak correlation, or bad fit)

p. 125: 6-10 EVEN

We then listened to the first 30 minutes of the following podcast as an introduction to logarithms: http://www.radiolab.org/story/91697-numbers/

We then introduced logarithms and proved various properties.

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