Chapter 7: Powers

Chapter 7 Preview: aa Chapter 7 Preview.pdf
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Wiki Summary Assignments

7-1: Jeremiah B. and Emma R.
7-2/7-3: Courtney G. and Trisha T.
7-4: Jacob R. and Jessica R.
7-5: Ryan B. and Tyler Y.
7-6: Amira A. and Christian S.
7-7/7-8: Nate J. and Nick Y.

Section 7-1: Power Functions

Notes: aanotes7-1.pdf

Lesson 7-1 was an introduction to power functions. Exponentiation, or powering, is where a base is taken to an exponent.
For example, x², where x = the base (the number being multiplied over and over) and ² = the exponent (the number of factors of the base.) There are six functions we learned. The first, the original power function, reads f(x) = x^n where n > 0. The next five (identity, squaring, cubing, fourth power, and fifth power functions) have the value of n go up by one each time. Then, we learned about graphing these functions. If the exponent (n) is odd, R = {y:y is all real numbers} and it has rotational symmetry about the origin. If the exponent (n) is even, R = {y:y»0}.
-Emma R

Lesson 7-1 was about Power Functions. Exponentiation, or powering, is when the base is taken to an exponent. Let's take x^n. The base is "x" and the Exponent is the "n" and together they make a power, thus we call this exponentiation, or powering. The Base is the number multiplied over and over. The Exponent is the number of factors of the base. A power function is f(x)= X^n when n > 0. f(x) = x^1, which is called an Identity Function. A Squaring Function is f(x) = x^2. This goes on and on as the Exponents get bigger (i.e. cubing, fourth, and fifth power functions). When graphing there are a few properties to consider. The graph goes through the origin when 0^n = 0 for all n > 0. The Domain is all Real Numbers. The Range has two possibilities. If "n" is odd, R = {y:y is all Real numbers} and If "n" is even, R = {y:y greater than or equal to 0}. Symmetry exist in two places. When "n" is odd ( there is Rotaional Symmetry about the origin) and when "n" is even (there is Reflection Symmetry over the y-axis).

-Jeremiah B.

Section 7-2/7-3: Properties of Powers
Notes: aanotes7-2.pdf

In chapter 7, lessons 2 and 3, we examined the many power postulates. We first learned the Product of Powers Postulate which states: b^m · b^n = b^m+n. Using this postulate, we can solve the equation 4^2 · 4^8 = 4^10. Next we learned the Power of a Power Postulate which states: (b^m)^n = b^m·n. To show this postulate look at the equation (2^3)^2. Written out it would be (2^3)(2^3) or 2·2·2·2·2·2 which equals 2^6. We can simplify this process by using the the Power of a Power Postulate. So (2^3)^2 = 2^3·2 = 2^6. After that we found that when we solve a problem in the form of (ab)^m, we can use the Power of a Product Postulate which states: (ab)^m =
a^m · b^m. We can automatically simplify (5x)^2 to 25x^2. In this example make sure you don't forget to multiply the 5 as it is also in the parentheses. The Quotient of Powers Postulate, b^m ÷ b^n = b^m-n, makes it easy to simplify problems such as 3^18 ÷ 3^17 = 3^18-17 = 3^1 = 3. When you see the form (a÷b)^n it equals a^n ÷ b^n.The Zero Exponent Theorem tells you that any number to the power of zero equals 1. Lesson two just dealt with negative integer exponents, teaching you that b^ -n = 1/ b^n. So every time you see a negative exponent you it from the numerator to the denominator or vice versa and you take away the negative sign. Make sure you remember that there are multiple ways of solving problems where more than one of these postulates apply and some ways are easier than others so write out your steps to keep track of your values. Trisha T.

Section 7-4: Compound Interest

Notes: aanotes7-4.pdf

In this lesson we learned about compound interest. We setup a formula A=P(1+r)^t to calculate annual interest, where A=total amount P=principal(starting amount) r=interest rate t=time in years. This calculation uses the method of compounding, earning interest on interest. It also uses powering/exponentiation or multiplying a number by itself. We later setup another formula for interest that is not annual A=P(1+r/n)^nt [n=number of times compound per year]. With these two equations you can calculate the interest in almost any type of savings or checking account. -Jacob R.

Section 7-5: Geometric Sequences

Notes: aanotes7-5.pdf

Section 7-6: nth Roots

Notes: aanotes7-6.pdf

In this lesson we learned about how to relate a music scale to n^th root. When you have a number like 25^3/2 there is different ways you can solve it. You can solve it as (25^1/2)^3 or by (25^3)^1/2. when you have something like x^12 = 2 you can set it up as a system of equations. y = x^12 y = 2 you can put it in your calculator then graph it. when it is graphed then you find the intersects. then that is the answer to your equation. - Tyler Y.

Section 7-7/7-8: Rational Exponents

Notes: aanotes7-7-8.pdf