# Chapter 8 (Alg 2) Flashcards

Exponential function

y = ab^x where a DNE 0 and b>1

Exponential growth function

if a > 0, b > 1 for a Exponential Function, y grows as x increases {} Graph rises from left to right graph passes through o,a and 1,ab Domain is all real numbers range is y > 0

Asymptote

A line that a graph approaches more and more closely

The x-axis is an asymptote of the graph of y = ab^x

Exponential decay function

y = ab^x where a > 0 and 0 0

Exponential growth, Exponential decay

y = a(1 + r)^t

y = a(1 - r)^t

a is the initial amount, r is the percent increase or decrease written as a decimal, t is the number of time periods

Growth factor

The quantity of (1 + r)

Decay factor

The quantity of (1 - r)

Compound Interest

Initial principal P deposited in an account that pays interest at an annual rate r (expressed as a decimal), compounded n times per year on previously earned interest

Amount a in the account after t years can be modeled

A = P(1 + r/n)^nt

natural base e

Euler’s number

irrational, defined as followed,

as n approaches + inf. (1 + 1/n)^n

Common Logarithm

log with base 10 simply denoted by log

Logarithm of y with base b

denoted by log base b of y

Defined as log base b of y = x if and only if

b^x = y

Special Logarithm Values

Log of 1 {} log base 1 = 0

Logarithm of base b {} log base b = 1

Inverse Functions

g(f(x)) = log base b of b^x = x f(g(x)) = b^log base b of x = x

Graphing logarithmic Functions

the graph of y = log base b of x is the reflection of the graph of y = b^x in the line y = x

The graph of y = log base b of x includes (1,0) and (b,1)

The y-axis is a vertical asymptote

The domain is x > 0, and the range is all real numbers

To graph logs

y = log base b (x - h), translate the graph of y = log base b of x horizontally h units. y = log base b of x + h, translate the graph of y = log base b of x vertically k units