algebra i chapter 7 notes rules of exponents. section 7-1 monomial – constant – base –...

Algebra I Chapter 7 Notes

Rules of Exponents

Section 7-1

Monomial –

Constant –

Base –

Exponent -

Section 7-1

Monomial – a number, a variable, or the product of a number and variable with non-negative, integer exponents

Constant – a monomial that is a real number

Base – term being multiplied in an exponential expression

Exponent – the number of times the base is multiplied in an exponential expression

Section 7-1: Multiplication Rules of Exponents, Day 1

Ex) Determine whether each expression is a monomial. Write yes or no, explain WHY.a) 10 b) f + 24 c) d)

e) -5y

Section 7-1: Multiplication Rules of Exponents, Day 1Product of Powers

Ex) Simplify each expressiona) b)

c)

Words To multiply two powers that have the same base, you add their exponents

Symbols For any real number a, and any integers m and p:

Examples


Power of a Power

Ex) Simplifya) b)

Words To raise a power to another power, you multiply the exponents

Symbols For any real number a, and any integers m and p,

Example


Power of a Product

Ex) Simplify each expressiona) b)

c) d)

Words Exponents can be distributed when terms are being multiplied

Symbols For any real numbers a and b, and any integer m,

Examples


Ex) Use all rules to simplifya) b)

c) d)

Section 7-2: Division Rules of Exponents, Day 1

Quotient of Powers

Ex. Simplifya) b)

c)

Words To divide two powers with the same base, subtract the exponents

Symbols For any nonzero number a, and any integers m and p,

Examples


Power of a Quotient

Ex) Simplifya) b)

c) d)

Words To find the power of a quotient, find the power of the numerator and the power of the denominator

Symbols For any real numbers a and b does not = zero, and any integer m,

Examples


Simplify using division rules of exponents1) 2)

3)

4) 5)6)


Zero Exponent Property

Ex) Simplify. Assume no denominator = zeroa) b)

c)

Words Any nonzero number raised to the zero power is equal to 1

Symbols For any nonzero number a,

Example


Negative Exponent Property

Ex) Simplify. NO NEGATIVE EXPONENTS!a) b)

c) d)

Words For any nonzero number a, and any integer n, is the reciprocal of

Symbols For any nonzero number a and integer n,

Examples or


Simplify using division rules of exponents1) 2)

3) 4)

Section 7-4: Scientific Notation

Scientific Notation – a number written in the form , where 1 < a < 10 and n is an integer.Ex) Write the following numbers in scientific notation.1) 201,000,000 2) 0.000051

Section 7-4: Scientific Notation

Ex) Write the following numbers in standard form1) 2)

Section 7-4: Multiplying with Scientific Notation

Ex) Use rules of exponents to multiply the following numbers together. Express your answer in both scientific notation and standard form!1)

2)

Section 7-4: Dividing with Scientific Notation

Ex) Use rules of exponents to multiply the following numbers together. Express your answer in both scientific notation and standard form!1)

2)

Section 7-5: Exponential Functions – Exponential Growth, Day 1

Exponential Function – A function that can be written in the form , where a cannot be 0, b > 0, and b cannot be 1. Examples of exponential functions: , , or

Exponential GrowthEquation where

Domain and Range

Intercepts

End Behavior


Graph of Exponential Growth


Ex) Graph , Find the y-intercept, and state the domain and range. You will have to create a table to graph! What is the pattern on the table?

x y

-2

-1

0

1

2

Section 7-5: Exponential Functions – Exponential Decay, Day 2

Exponential DecayEquation where

Domain and Range

Intercepts

End Behavior


Graph of Exponential Decay


Ex) Graph , Find the y-intercept, and state the domain and range. You will have to create a table to graph! What is the pattern on the table?

x y

-2

-1

0

1

2

Section 7-6: Exponential Growth and Decay Patterns, Day 1

Equation for Exponential Growth:a: initial amount t : time y: final amountr: rate of change expressed as a decimal, r > 0

Ex) The prize for a radio station contest begins with a $100 gift card. Once a day, a name is announced. The person has 15 minutes to call or the prize increases 2.5% for the next day.a) Write an equation representing the amount of the gift card after t days with

no winnerb) How much will the card be worth if no one claims it after 10 days?


Compound Interest – interest earned or paid on both the initial investment AND previously earned interest. It is an application of exponential growth.

Equation for Compound Interest

A: current amount P: principal/initial amountr: annual interest rate expressed as a decimaln: number of times interest is compounded per yeart: time in years


Ex) Maria’s parents invested $14,000 at 6% per year compounded monthly. How much money will there be in the account after 10 years?


Equation for Exponential Decay

a: initial amount y = final amountt: time r: rate of decay as a decimal 0 < r < 1Ex) A fully inflated raft is losing 6.6% of its air every day. The raft originally contained 4500 cubic inches of air.a) Write an equation representing the loss of airb) Estimate the amount of air in the raft after 7 days


Solve the 3 problems. You must choose which equation to use on each.1) Paul invested $400 into an account with 5.5% interest compounded monthly.

How much will he have in 8 years?

2) Ms. Acosta received a job as a teacher with a starting salary of $34,000. She will get a 1.5% increase in her salary each year. How much will she earn in 7 years?

3) In 2000 the 2200 students attended East High School. The enrollment has been declining 2% annually. If this continues, how many students will be enrolled in the year 2015?

algebra i chapter 7 notes rules of exponents. section 7-1 monomial – constant – base –...

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