Flashcards in Algebra 2: Chapter 7 Deck (17):

1

##
what equation is used when modeling growth/decay situation?

what does everything stand for?

###
A(t) = a (1 +/- r)^t

A = final amount

a = initial amount

+/- = growth (+), decay (-)

r = rate of increase (do percent in decimal form)

t = # of time periods

2

## what is the inverse of f(x) = x/8?

### f^-1(x) = 8x

3

##
when writing the inverse of a table of functions....

(domain and range..?)

### write the domain and range in numerical order (least --> greatest), but graph it like you would the regular table of x and y values, except put the y-values as the x-values, and vice-versa

4

##
what is the product property of logarithms?

when is this used?

###
log b MN = log b M + log b N (and vice-versa)

to express a SINGLE logarithm

5

## what is the quotient property of logarithms?

### log b (M / N) = log b M - log b N

6

## what is the power property of logarithms?

###
log b A^p = P log b A

P = power

7

## what is the inverse property of logarithms?

### log b B ^x = X or B^log b X = X

8

## how is a base of a logarithm function changed into a base of 10?

### log b X = (log a X) / (log a B)

9

## how do you solve an exponential equation? (2 methods)

###
1. write them so all of the bases are the same

ex. if B^x = B^y, then X = Y

2. take the log of BOTH sides

ex. if A = B, then log A = log B

10

## what do you do when you have (X^a) ^b ?

### you MULTIPLY the exponent, so it is... X^ab

11

## how do you solve logarithm equations?

### if log b X = log b Y, then X = Y

12

## properties of e? (2)

###
- approx. 2.72

- it's the base of the NATURAL log --> log e *base* = ln (not common log)

13

## what is the natural log?

###
ln ---> log e *base* = ln

***Don't write log e.

14

##
which equation do you use for continuous compounds...?

what do the letters stand for?

###
A = Pe^rt

A = current amount

P = principal amount (initial amount)

r = rate (expressed in decimal form)

t = time (ie. amount of years, days, hours, etc.

15

##
which equation is used to calculate half-lifes?

what does everything stand for?

###
N(t) = No e ^-kt

N(t) = amount REMAINING

No = initial amount (grams)

-k = decay constant

t = time

16

##
when calculating half-lives, what do you do in order to find the decay constant (-k)?

[4 STEPS]

Use this for an example:

An element has a half-life of 15,000 years. How much of a 3gram sample is left after 12,000 years?

###
1. put everything equal to 1/2

* 1/2 = 1e ^ -k(15,000)

2. give both sides ln

* ln(1/2) = ln e (-k)(15,000)

3. ln e cancel each other out, so the equations is...

* ln (1/2) = -15,000k

4. divide 15,000 by ln (1/2)

* -k = 4.62 x 10^-5

17