24 terms

# Chapter 8: Exponents and Exponential Functions

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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)