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What is an example of an exponential function used in real-world applications? Show a
math example how it is used. Describe why that application is important.
Compound Interest formula
A = P(1 + r/n)^nt
The principal is the initial amount of m
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Share important information and learning from this website with your class members.
What is most beneficial for you?
Purple Math web-site link to the Inverse Function was under the advanced algebra topic.
The information I got from it is how t
Solve the equations.
1. 4 x + 3 = 2 x 33
4 x + 3 = 2 x 33
4 x + 3 + 2 x = 2 x 33 + 2 x
6 x + 3 = 33
6 x + 3 3 = 33 3
6 x = 36
6 x 36
=
6
6
x = 6
2. m 12 = 7m + 44
m 12 = 7 m + 44
m 12 7 m = 7 m + 44 7 m
8m 12 = 44
8m 12 + 12 = 44 + 12
8m = 56
8m 56
=
8
Sometimes you can simplify an expression by
distributing and combining like terms.
Simplifying by Distributing:
Step 1
Distribute by multiplying each term by the number
outside the parentheses.
-4 5x^3 4 -2x^2 4 3x 4 -1
Step 2
Multiply the numbers within
The property that allows you to change the order of
the terms when adding or multiplying is called the
commutative property. This property states that you
can change the order of the terms in addition and
multiplication problems and still get the same res
Exponents give us a way to write numbers in a
shorter form. The exponential form of each number
includes a base of 2, and an exponent that
represents the number of hours that have elapsed
since the starting time.
Using exponents gives you another way to w
The associative property allows you to change how
numbers are grouped in addition and multiplication
problems. Parentheses are often used to show how
numbers are grouped.
Remember that parentheses are not only used to
show how terms are grouped, they are
What do constants look like in algebra?
Any number, such as 2, 100, or -205 is considered a
constant. The value of each number never changes.
After all, 2 is always 2, and 100 is always 100.
What do variables look like in algebra?
Variables are usually le
Any change you make to one side of an equation
must also be made to the other side. This rule is
called the property of equality.
In an equation, the missing number is represented
by a variable. To solve an equation with a variable
using algebra, you need
If you can see a pattern in a table of values, you can
translate that pattern into an algebraic expression.
Before you can write an algebraic statement, though,
you need to choose the variables that you will use.
Example:
Cory kept track of how far he dro
Remember that parentheses are another way to
express multiplication. Whenever you see a number
outside of terms that are added or subtracted and
grouped within parentheses, you can multiply that
number by each term in the group.
Whenever you see a number
In algebra, you will need to translate words and
phrases into algebraic expressions. Some common
words and phrases can be translated directly into
mathematical symbols.
How can you translate the following statement into
an algebraic expression? The produc
In math, a property of numbers is something that is
always true about them.
The additive inverse of a number is the same number
with the opposite sign. When adding a number to its
additive inverse, the sum will always be 0. This is the
additive inverse pr
In math, an identity is a number that you can add or
multiply to another number and not change the
original number.
The additive identity is 0 because you can add 0 to
any number and the sum is the number you started
with.
The multiplicative identity is 1
A number line gives us a way to show real numbers ,
or the numbers we encounter every day, visually.
Points are plotted on the number line according to
the value of the number, similar to how events are
placed on a time line based on a date. The location
A word that is commonly used when talking about
roots is radical . You may have heard the word
radical used to describe an awesome skateboard
trick, but in math radical means "root." The symbol
is called a radical sign. A number that appears under
the rad
The area of a square is found by multiplying the
length of the side by itself. Whenever you are
multiplying a number by itself, you can use a power
of 2 to represent the repeated multiplication.
The number 1 raised to any power is 1.
Any nonzero number ra
In any mathematical expression, the operations must
always be done in the same order. First, simplify any
expression inside of parentheses. Next, simplify any
exponents . The next operations, multiplication and
division, are done together from left to rig
When you cube a number, you multiply it by itself 3
times.
23 = 2 2 2 = 8
Another common type of radical is the cube root .
The cube root has an index of 3. Taking the cube root
of a number can be thought of as the opposite of
raising a number to the thir
A mathematical set is just a list of items, separated
by commas, and written between cfw_ symbols. Each
item in a set is called an element . For example, the
set of even numbers between and including 1 and 11
can be written as cfw_2, 4, 6, 8, 10.
Two set
The numbers that you use for counting are called the
natural numbers. Natural numbers include 1, 2, 3, 4,
5, and so on.
To describe how many people are sitting in the
theater, we can use whole numbers, which include
all of the natural numbers and 0.
Numbe
Comparing decimal numbers involves looking
carefully at the place values in each number.
When you compare two decimal numbers to each
other, you can tell which number is larger and which
is smaller by looking at the corresponding place
value positions. Ea
Fractions can be represented in various forms, but
there is only one way to write a fraction in its
simplest form. Simplest form is a way to write the
fraction without any common factors in its
numerator and denominator.
Why bother simplifying a fraction
In a terminating decimal, the numbers after the
decimal point end, rather than continuing forever.
A non-terminating decimal never ends. The
numbers after the decimal point keep going on and
on. Instead of taking up a whole page (or more!) to
write a non-
To find the equivalent decimal form of a fraction,
divide the numerator by the denominator.
To change a number from a terminating decimal to a
fraction, you need to determine what numbers will
go in the numerator and denominator of the
fraction. The numer
A mixed number is made up of a whole number and
a fraction. It actually means that a whole number is
added to a fraction even though there is no addition
sign.
Improper fractions , where the numerator is larger
than the denominator , can also be written a
Writing Numbers in Expanded
Form
_
*A number written out showing the sum of
each place value in the number is a
number in expanded form*
1. 7,321 = 7,000 + 300 + 20 + 1
2. 5,692 = 5,000 + 600 + 90 + 2
3. 741 = 700 + 40 + 1
4. 72,655 = 70,000 + 2,000 + 600
Estimation in Addition
_
*Estimation an answer to a problem is a
way of getting an approximate sum. To
estimate the sum, round the addends. The
answer should be fairly close to the actual
sum*
Examples: rounded to the nearest ten
1. 4,537 + 498 = ? ; 4,54
Less Than and More Than
Numbers
_
*Less than is < as in 1 < 2. Greater than is
> as in 2 > 1*
1. 23 < 54
2. 14 < 60
3. 3 > 2
4. 5 < 15
5. 64 > 60
6. 64 < 98
7. 57 < 85
8. 32 > 21
9. 34 > 30
10. 45 < 50