Flashcards in PreCalc Chapter 3 Test Deck (48)

Loading flashcards...

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