what are the logarithmic models?

y=a+bLnx

y=a+blogx

what is the equation for exponential growth?

decay?

what does each variable stand for

A=Ie^kt and A=le^-kt A is what you have (dependent) I is your initial amount e is 2.71828 (constant/base/multiplier) k is constant of exponentialism (constant coefficient/growth rate) and t is time (independent)

An exponential growth model has the form ______, and an exponential decay model has the form_________.

y=ae^bx or A=Ie^kt

y=ae^-bx or A=Ie^-kt

in probability and statistics, Gaussian models commonly represent populations that are ___________ _____________.

normally distributed

a logistic growth model has the form

y=a/1+be^-rx

a logarithm is an _____

exponent

logarithmic and exponential equations are _______

inverses

the parent log has an assumed base of ____

the natural log has an assumed base of __

10 (common log)

e

what does e=

2.71821

logarithmic graphs have a ____ asymptote (__=#) while exponential graphs of a ____ asymptote (__=#)

vertical x

horizontal y

is e a variable?

no, it is a constant

what is true of all logarithmic graphs?

how do you restrict the domain?

how do they look?

they all pass vertical line test, always have x-intercept and asymptote

you cannot take the log of 0 or a negative number

boomerang

how you know if an equation is exponential

it has a variable as an exponent

what would you do with

y=2^-x^2

take the square of the number first then multiply by the implied negative one

how would you simplify 3^x-2

3^x3^-2

3^x(1/9)

like terms have the same ____ and same _________

base, exponent

polynomial functions are examples of ___ functions

algebraic

exponential and logarithmic functions are examples of nonalgebraic functions, also called _____ functions

transcendental

you can use the _______ Property to solve simple exponential equations

one-to-one

the exponential function f(x)=e^x is called the ______ _____ function, and the base e is called the ______ base

natural exponential, natural

to find the amount A in an account after t years with principal P and an annual interest rate r compounded n times per year, you can use the formula______________.

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

to find the amount A in an account after t years with principal P and an annual interest rate r compounded continuously, you can use the formula _____________.

A=Pe^rt

the inverse function of the exponential function f(x)=a^x is called the ______ function with base a

logarithmic

the common logarithmic function has base

10

the logarithmic function f(x)+lnx is called the ______ logarithmic function and has base _________

natural, e

the inverse properties of logarithms state that logaA^x=x and

a^logaX=X

to one-to-one property of natural logarithms states that if Inx=Iny, then_______________

x=y

the domain of the natural logarithmic function is the set of __________ ________ __________.

positive real numbers

all real numbers such that x is greater than 0

to evaluate a logarithm to any base, use the ______ formula

change-of-base

the change-of-base formula for base a is given by logaX=__________

logbX/logbA

you can consider logaX to be a constant multiple of logbX; the constant multiplier is ______________

1/logbA

what is the product property of logs

goes to addition

log4X*y^2=log4X+log4Y^2

what is the quotient property of logs

to difference

log7 x^3/y=log7X^3-log7Y

what is the power property of logs

logx^4=4*logx

(make sure you only bring it out if it is for the WHOLE THING

while doing the change-of-base formula, do you use the natural log or the common log

it does not matter as long as you are consistent

how can you make powers roots and roots powers

the cubed root equals ^1/3 and so on

how do you solve exponential or logarithmic (or any, really) equation

use inverse operations

your equation is done when _ is by itself

x

what is the log of 625 to base 5

what is the log of .001

4, -4

when solving an equation, it is important to check for _____________ by plugging your solutions back into the original equation

extraneous

when you are told to find an exponential model, make sure you have all variables expect____

the x and y, or the A and t

for like terms with the same base and exponent, when multiplying, add exponents but ______________________ the bases

do not do anything with the bases

asymptotes begin with _________________________.

x= or y=

if you have a log that can be taken by reducing the number, what do you do

reduce it, multiply it by the number you reduced it by, separate by addition, and finish

remember to use ________ when you are solving logs to indicate separation

parentheses

when simplifying logs, make sure to use parentheses between subtraction and addition and also make sure that the log of a certain number–make sure that number cannot be divided by anything to get a whole number answer. if it can, multiply and add based on rules of expansion

..

when solving an exponential equation, take the ___ of both sides

log

half life equations are decay, meaning k is

negative