Algebra Chapter 7 Notes
Exponents and Exponential Functions
7.1 Apply Exponent Properties Involving Products
Order of magnitude: ______
______
Power: ______
Exponent: ______
Base: ______
Product of Powers Property: ______
Simplify the expressions:
a.26∙ 28b.(–3)7 ∙ (–3)
- (–7)3 ∙ (–7) ∙ (–7)4d. m ∙ m5 ∙ m6
Power of a Power Property: ______
Simplify the expressions:
a.(33)6 b.[(–12)7]6
c.(d5)2d.[(x – 3)3]4
Power of a Product Property: ______
Simplify the expressions:
a.(16 ∙ 21)4b.(6mn) 3
c.(–5p) 3d.–(2q)4
Use all three properties
Simplify (–3y5)3 • 2y2.Simplify • d
7.2 Applying Exponent Properties Involving Quotients
Quotient of Powers Property: ______
Simplify the expressions.
a. b.
c. d.
Power of a Quotient Property: ______
Simplify the expressions.
a. b.
Use the properties of exponents: Simplify the expressions.
a. b.
Solve a real world problem:Distances The distance from Earth to the nearest galaxy is about 1022 meters. The distance from Earth to the North Star is about 1019 meters. How many times further from Earth is the nearest galaxy than the North Star?
7.3 Define and Use Zero and Negative Exponents
Zero exponents: ______
Evaluate the expressions.
a.150b.c. (-6)0
Negative exponents: ______
Evaluate the expressions.
a.4–3 b.
c. (–5)–4d.
Evaluate exponential expressions.
a. 1316 • 13–14b. [(–2)–4]2
c.(–4)7 • (–4)–9d.
Use properties of exponents: Simplify the expression. Write your answer using only positiveexponents.
a.(3m–2n)3 b. (5x2y–3z)4
c. d.
Remembering the exponent properties:
Zero ExponentNegative Exponent
Product of Powers
Quotient of Powers
Power of a Power
Power of a Product
Power of a Quotient
7.4 Write and Graph Exponential Growth Functions
Exponentialfunction: ______
Exponential growth: ______
Compound interest: ______
Example 1: Write a rule for the function.
Example 2: Graph the function y = 5 • 3x. Identify its domain and range.
x / –2 / –1 / 0 / 1 / 2y
EXAMPLE 3: Graph y = –• 4x and y = 2 • 4x. Compare each graph with the graph of y = 4x
x / y = 4x / y =•4x / y = 2•4x–2
–1
0
1
2
Exponential Growth Model: ______
Example 4: The owner of an original copy of a 1938 comic book sold it at an auction in 2005 The owner bought the comic book for $55 in 1980. The value of the comic book increased at a rate of 2.8% per year.
a. Write the function that models the value of the comic book over time.
b. What was the approximate value of the comic book at the time of the auction in 2005? Round your answer to the nearest dollar.
Example 5: You put $125 in a savings account that earns 2% interest compounded yearly. You do not make any deposits or withdrawals. How much will your investment be worth in 5 years?
7.5 Write and Graph Exponential Decay Functions
Exponential decay: ______
Example 1: Tell whether the table represents an exponential function. If so, write a rule for the function.
x / –1 / 0 / 1 / 2y / / –2 / –12 / –72
Example 2:Graph the function y = . Identify its domain and range.
x / –1 / 0 / 1 / 2y
Example 3: Tell whether the graph represents exponential growth or exponential decay. Then write a rule for the function.
a.b.
Exponential Decay Model: ______
Example 5: A farmer bought a tractor in 1999 for $30,000. The value of the tractor has been decreasing at a rate of 18% per year.
a. Write a function that models the value of the tractor over time.
b. What was the approximate value of the tractor in 2005?