Chapter 8: Exponents and Exponential Functions

24 terms by msmmwelch

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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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