Chapter 8: Exponents and Exponential Functions
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Created by:
itssimi on January 17, 2012
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Description:
Key vocabulary and properties from Chapter 8 of McDougal Littell Algebra I. This chapter covers exponents, exponent properties, zero and negative exponents, scientific notation, and growth and decay functions.
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24 terms
Terms | Definitions |
|---|---|
 order of magnitude | the power of 10 nearest a quantity |
| power | the number of times a quantity is used as a factor |
| exponent | a mathematical notation indicating the number of times a quantity is used as a factor |
| base | the number or expression that is used as a factor in a repeated multiplication |
| Product of Powers Property | to multiply powers having the same base, add the exponents a^m x a^n = a^m+n |
| Power of a Power Property | to find a power of a power, multiply exponents (a^m)^n = a^mn |
| Power of a Product Property | to find a power of a product, find the power of each factor and multiply (ab)^m = a^m b^m |
| Quotient of Powers Property | to divide powers having the same base, subtract exponents a^m/a^n = a^m-n |
| Power of a Quotient Property | to find a power of a quotient, find the power of the numerator and the power of the denominator and divide (a/b)^m = a^m/b^m |
| Zero Exponent | a to the zero power is 1 a^0 = 1 |
| Negative Exponent | a^-n is the reciprocal of a^n a^-n = 1/a^n |
| reciprocal | opposite |
| cube root | the base of a cube (a quantity to the power of 3) b^3 = a, then b is the ___ ___ of a |
| scientific notation | a number in the form c x 10^n |
| exponential function | a function in the form y = ab^x; nonlinear |
| exponential growth | a graph that rises from the left;when a quantity grows exponentially, represented by y = ab^x |
| initial amount | what "a" represents in the model y = a(1 + r)^t |
| growth factor | what "1 + r" represents in the model y = a(1 + r)^t |
| growth rate | what "r" represents in the model y = a(1 + r)^t |
| time period | what "t" represents in the model y = a(1 + r)^t |
| compound interest | interest earned on both an initial investment and on previously earned interest |
| exponential decay | a graph that falls from left to right, represented by the function y = ab^x |
| decay factor | what "1 - r" represents in the model y = a(1 - r) |
| decay rate | what "r" represents in the model y = a(1 - r) |
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