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Unit 6 Learning Targets
LT 6-1: I can use properties of exponents to simplify expressions and solve.
LT 6-2: I can simplify expressions involving zero and negative exponents.
LT 6-3: I can use an exponential model to represent change.
LT 6-4: I can identify exponential growth and decay.
LT 6-5: I can write a geometric sequence.
LT 6-6: I can transform exponential graphs.
LESSON 6-1
LESSON 6-1
Rational Exponents and Properties of Exponents
Rational Exponents and Properties of Exponents
Radicals can be rewritten using rational exponents. The properties of exponents can be used to solve equations with rational exponents.
Help Videos:
● What Are Rational Exponents?
● What Are the Properties of Rational Exponents?
Practice:
6-1 Math XL
LESSON 6-2
LESSON 6-2
Radical Expressions
Radical Expressions
Properties of exponents are used to rewrite radical expressions in different forms. A radical expression is written in the simplest form when there are no perfect square factors other than 1 in the radicand.
Help Videos:
● What Is the Product Property of Square Roots?
● How Do You Multiply Two Radicals?
Practice:
6-2 Math XL
LLESSON 6-3
LLESSON 6-3
Exponential Functions
Exponential Functions
An exponential function models the relationship between two quantities that differ by a constant ratio. Exponential functions are modeled using f(x)=a(b)^x
where a is the initial amount and b is the constant ratio.
Help Videos:
● How Do You Graph an Exponential Function Using a Table?
Practice:
6-3 Math XL
LESSON 6-4
LESSON 6-4
Exponential Growth and Decay
Exponential Growth and Decay
An exponential growth function increases by a fixed percent over each interval. An exponential decay function decreases by a fixed percent over each interval. Exponential growth and decay functions can be used to model many real-world situations.
Help Videos:
● How Do You Solve a Word Problem with Exponential Decay?
Practice:
6-4 Math XL
LESSON 6-5
LESSON 6-5
Geometric Sequences
Geometric Sequences
Geometric sequences are number sequences in which each term is related to the next by a common ratio. They can be represented by recursive and explicit formulas. Exponential functions can represent geometric sequences.
Help Videos:
● How Do You Find the Common Ratio of a Geometric Sequence?
● How Do You Find the nth Term in a Geometric Sequence?
Practice:
6-5 Math XL
LESSON 6-6
LESSON 6-6
Translations of Exponential Functions
Translations of Exponential Functions
The values of the constants h and k affect the graphs of exponential functions. Changing the value of k results in a vertical shift in the function’s graph. Changing the value of h results in a horizontal shift in the function’s graph.
Help Videos:
● What Does the Constant h Do in the Exponential Function ?
● What Does the Value of k Do in the Exponential Function ?
Practice:
6-6 Math XL
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