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21 terms

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.