APPC 7-8 NEW

Algebraic Functions

A function with values that are obtained by adding, subtracting, multiplying, or dividing constants and the independent variable or raising the independent variable to a rational power

Transcendental Functions

A function that cannot be expressed in terms of algebraic expressions, such as the exponential or logarithmic function

Exponential Functions

A function of the form f(x)=ab^x, where x is any real number and a and b are real number constants such that a is not 0, b is positive, and b not 1

Natural Base

The irrational number e, which is approximately equal to 2.718281828...

e = lim(1+ 1/x)x

Continuous Compound Interest

Interest that is reinvested continuously so that there is no waiting period between interest payments. Formula is A=Pe^rt

Compound Interest Formula

P is principal invested, r is annual rate, n is number of times compounded annually, and A is account balance A = P (1 + r/n )^nt

Logarithmic Function

A function of the form y = logb x , where b>0, b not 1, and x>0, which is the

inverse of the exponential function of the form by = x

Common Logarithm

A logarithm with base 10, usually written log x

Natural Logarithm

A logarithm with base e, written ln x

Change of Base Formula

For any positive real numbers a, b, and x, a not 1, b not 1

log b x = log a x/ log a b