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Math Chapter 3 Vocab

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PLAY
algebraic
Polynomials and rational functions are examples of ___ functions.
transcendental
Exponential and logarithmic functions are examples of nonalgebraic functions, also called ___ functions.
natural exponential, natural
The exponential function given by e^x is called the ___ ___ function, and the base e is called the ___ base.
A=Pe^rt
To find the amount A in an account after t years with principle P and an annual interest rate r compounded continuously, you can use the formula ___.
logarithmic
The inverse function of the exponential function given by a^x is called the ___ function with base a.
10
The common logarithmic function has base ___.
natural, e
The logarithmic function given by ln(x) is called the ___ logarithmic function and has base ___.
a^(loga(x))=x
The Inverse Property of logarithms and exponentials states that loga(a^x)=x and ___.
x=y
The One-to-One Property of natural logarithms states that if ln(x)=ln(y), then ___.
Change-of-base
To evaluate a logarithm to any base, you can use the ___ formula.
logx/loga
The change-of-base formula for base e is given by loga(x)=___.
Power Property
ln(u^n)=n ln(u) is the ___ ___.
Product Property
loga(uv)=loga(u)+loga(v) is the ___ ___.
Quotient Property
loga(u/v)=loga(u)-loga(v) is the ___ ___.
solve
To ___ an equation in x means to find all values of x for which the equation is true.
extraneous
A(n) ___ solution does not satisfy the original equation.
y=ae^bx, y=ae^-bx
An exponential growth model has the form ___ and an exponential decay model has the form ___.
y=a+b lnx, y=a+b logx
A logarithmic model has the form ___ or ___.
normally distributed
Gaussian models are commonly used in probability and statistics to represent populations that are ___ ___.
bell, average value
The graph of a Gaussian model is ___ shaped, where the ___ ___ is the maximum y value of the graph.
sigmoidal
A logistic curve is also called a ___ curve.