Exploring Exponential Models
Exponential function: is a funtion with the general form of y = ab^x
Growth factor: when b>1
Decay factor: when b <1
Asymtote: is a line that a graph approches as "x" or "y" increases in absolute value.
Properties of Exponential Functions
A = Pert A: amount in account P: Principle r: annual rate of intrest t: time in years
Logarithmis Functons as Inverses
Logarith: the base of a positive number.
Common logarith: is a logarithm that uses the base ten.
Logarithmis function: is a inverse of a exponential function.
Ex. log y = x b
Properties of Logarithms
Product Property: log(b) MN = log(b)M + log(b)N
Quotient Property: log(b) M/N = log(b)M - log(b)N
Power Property: log(b) M^x = x log(b)M
Exponential and Logarithmis Equations
Exponential equation: an equation in the form, b^cx = a.
Change of base formula: to evaluate a logarithm with any base.
Logarithmis equation: a equation that contains a logarithmic expression.
Ex. 7^3x = 20
7^3x = 20 log7^3x = 20 3xlog7 = log20 x= log20/ 3log7 x=0.5132
Natural logarithm function: the functions inverse.
Ex. Write 3 ln 6 - ln 8 as a single natural logarithm
3 ln 6 - ln 8 = ln 6^3 - ln 8 Power Property = ln 6^3/8 Quotient Property = ln 27 Simplify