PreCalc Chapter 3 Test Flashcards Preview

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Flashcards in PreCalc Chapter 3 Test Deck (48)
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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