PreCalc Chapter 3 Test Flashcards Preview

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Flashcards in PreCalc Chapter 3 Test Deck (48)
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0
Q

what are the logarithmic models?

A

y=a+bLnx

y=a+blogx

1
Q

what is the equation for exponential growth?
decay?
what does each variable stand for

A
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)
2
Q

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

A

y=ae^bx or A=Ie^kt

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

3
Q

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

A

normally distributed

4
Q

a logistic growth model has the form

A

y=a/1+be^-rx

5
Q

a logarithm is an _____

A

exponent

6
Q

logarithmic and exponential equations are _______

A

inverses

7
Q

the parent log has an assumed base of ____

the natural log has an assumed base of __

A

10 (common log)

e

8
Q

what does e=

A

2.71821

9
Q

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

A

vertical x

horizontal y

10
Q

is e a variable?

A

no, it is a constant

11
Q

what is true of all logarithmic graphs?
how do you restrict the domain?
how do they look?

A

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
Q

how you know if an equation is exponential

A

it has a variable as an exponent

13
Q

what would you do with

y=2^-x^2

A

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

14
Q

how would you simplify 3^x-2

A

3^x3^-2

3^x(1/9)

15
Q

like terms have the same ____ and same _________

A

base, exponent

16
Q

polynomial functions are examples of ___ functions

A

algebraic

17
Q

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

A

transcendental

18
Q

you can use the _______ Property to solve simple exponential equations

A

one-to-one

19
Q

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

A

natural exponential, natural

20
Q

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

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

21
Q

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

A=Pe^rt

22
Q

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

A

logarithmic

23
Q

the common logarithmic function has base

A

10

24
Q

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

A

natural, e

25
Q

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

A

a^logaX=X

26
Q

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

A

x=y

27
Q

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

A

positive real numbers

all real numbers such that x is greater than 0

28
Q

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

A

change-of-base

29
Q

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

A

logbX/logbA

30
Q

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

A

1/logbA

31
Q

what is the product property of logs

A

goes to addition

log4X*y^2=log4X+log4Y^2

32
Q

what is the quotient property of logs

A

to difference

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

33
Q

what is the power property of logs

A

logx^4=4*logx

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

34
Q

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

A

it does not matter as long as you are consistent

35
Q

how can you make powers roots and roots powers

A

the cubed root equals ^1/3 and so on

36
Q

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

A

use inverse operations

37
Q

your equation is done when _ is by itself

A

x

38
Q

what is the log of 625 to base 5

what is the log of .001

A

4, -4

39
Q

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

A

extraneous

40
Q

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

A

the x and y, or the A and t

41
Q

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

A

do not do anything with the bases

42
Q

asymptotes begin with _________________________.

A

x= or y=

43
Q

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

A

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

44
Q

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

A

parentheses

45
Q

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

A

..

46
Q

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

A

log

47
Q

half life equations are decay, meaning k is

A

negative