Flashcards in PreCalc Chapter 3 Test Deck (48):

0

##
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)

1

## what are the logarithmic models?

###
y=a+bLnx

y=a+blogx

2

## 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

3

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

### normally distributed

4

## a logistic growth model has the form

### y=a/1+be^-rx

5

## a logarithm is an _____

### exponent

6

## logarithmic and exponential equations are _______

### inverses

7

##
the parent log has an assumed base of ____

the natural log has an assumed base of __

###
10 (common log)

e

8

## what does e=

### 2.71821

9

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

###
vertical x

horizontal y

10

## is e a variable?

### no, it is a constant

11

##
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

12

## how you know if an equation is exponential

### it has a variable as an exponent

13

##
what would you do with

y=2^-x^2

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

14

## how would you simplify 3^x-2

###
3^x3^-2

3^x(1/9)

15

## like terms have the same ____ and same _________

### base, exponent

16

## polynomial functions are examples of ___ functions

### algebraic

17

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

### transcendental

18

## you can use the _______ Property to solve simple exponential equations

### one-to-one

19

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

### natural exponential, natural

20

## 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

21

## 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

22

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

### logarithmic

23

## the common logarithmic function has base

### 10

24

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

### natural, e

25

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

### a^logaX=X

26

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

### x=y

27

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

###
positive real numbers

all real numbers such that x is greater than 0

28

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

### change-of-base

29

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

### logbX/logbA

30

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

### 1/logbA

31

## what is the product property of logs

###
goes to addition

log4X*y^2=log4X+log4Y^2

32

## what is the quotient property of logs

###
to difference

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

33

## 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

34

## 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

35

## how can you make powers roots and roots powers

### the cubed root equals ^1/3 and so on

36

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

### use inverse operations

37

## your equation is done when _ is by itself

### x

38

##
what is the log of 625 to base 5

what is the log of .001

### 4, -4

39

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

### extraneous

40

## 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

41

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

### do not do anything with the bases

42

## asymptotes begin with _________________________.

### x= or y=

43

## 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

44

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

### parentheses

45

## 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

### ..

46

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

### log

47