PreCalc Chapter 3 Test

Question 0

what are the logarithmic models?

Answer 0

y=a+bLnx

y=a+blogx

Question 1

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

Answer 1

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)

Question 2

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

Answer 2

y=ae^bx or A=Ie^kt

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

Question 3

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

Answer 3

normally distributed

Question 4

a logistic growth model has the form

Answer 4

y=a/1+be^-rx

Question 5

a logarithm is an _____

Answer 5

exponent

Question 6

logarithmic and exponential equations are _______

Answer 6

inverses

Question 7

the parent log has an assumed base of ____

the natural log has an assumed base of __

Answer 7

10 (common log)

e

Question 8

what does e=

Answer 8

2.71821

Question 9

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

Answer 9

vertical x

horizontal y

Question 10

is e a variable?

Answer 10

no, it is a constant

Question 11

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

Answer 11

they all pass vertical line test, always have x-intercept and asymptote
you cannot take the log of 0 or a negative number
boomerang

Question 12

how you know if an equation is exponential

Answer 12

it has a variable as an exponent

Question 13

what would you do with

y=2^-x^2

Answer 13

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

Question 14

how would you simplify 3^x-2

Answer 14

3^x3^-2

3^x(1/9)

Question 15

like terms have the same ____ and same _________

Answer 15

base, exponent

Question 16

polynomial functions are examples of ___ functions

Answer 16

algebraic

Question 17

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

Answer 17

transcendental

Question 18

you can use the _______ Property to solve simple exponential equations

Answer 18

one-to-one

Question 19

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

Answer 19

natural exponential, natural

Question 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______________.

Answer 20

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

Question 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 _____________.

Answer 21

A=Pe^rt

Question 22

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

Answer 22

logarithmic

Question 23

the common logarithmic function has base

Answer 23

10

Question 24

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

Answer 24

natural, e

Question 25

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

Answer 25

a^logaX=X

Question 26

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

Answer 26

x=y

Question 27

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

Answer 27

positive real numbers | all real numbers such that x is greater than 0

Question 28

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

Answer 28

change-of-base

Question 29

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

Answer 29

logbX/logbA

Question 30

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

Answer 30

1/logbA

Question 31

what is the product property of logs

Answer 31

goes to addition | log4X*y^2=log4X+log4Y^2

Question 32

what is the quotient property of logs

Answer 32

to difference | log7 x^3/y=log7X^3-log7Y

Question 33

what is the power property of logs

Answer 33

logx^4=4*logx | (make sure you only bring it out if it is for the WHOLE THING

Question 34

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

Answer 34

it does not matter as long as you are consistent

Question 35

how can you make powers roots and roots powers

Answer 35

the cubed root equals ^1/3 and so on

Question 36

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

Answer 36

use inverse operations

Question 37

your equation is done when _ is by itself

Answer 37

x

Question 38

what is the log of 625 to base 5 | what is the log of .001

Answer 38

4, -4

Question 39

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

Answer 39

extraneous

Question 40

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

Answer 40

the x and y, or the A and t

Question 41

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

Answer 41

do not do anything with the bases

Question 42

asymptotes begin with _________________________.

Answer 42

x= or y=

Question 43

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

Answer 43

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

Question 44

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

Answer 44

parentheses

Question 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

Answer 45

..

Question 46

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

Answer 46

log

Question 47

half life equations are decay, meaning k is

Answer 47

negative