## Correlation to Michigan Algebra 1 Standards

Section 13 Exponents and Exponential Systems

**Lessons: Properties of Exponents, Product Property - Multiplying Polynomials, Power of a Power Property, Power of a Product Property,
Combining the Multiplication Properties, Power of a Fraction Property, Quotient Property of Exponents (positive exponents), Quotient Property
of Exponents (positive and negative)**

A1.1.2 Know the properties of exponents and roots and apply them in algebraic expressions.

**L2.1.2** Calculate fluently with numerical expressions involving exponents. Use the rules of exponents, and evaluate numerical
expressions involving rational and negative exponents, and transition easily between roots and exponents.

**Lesson: Zero and Negative Exponents**

L1.1.4 Describe the reasons for the different effects of multiplication by, or exponentiation of, a positive number by a number less
than 0, a number between 0 and 1, and a number greater than 1.

**A1.1.2** Know the properties of exponents and roots and apply them in algebraic expressions.

**L2.1.2** Calculate fluently with numerical expressions involving exponents. Use the rules of exponents, and evaluate numerical
expressions involving rational and negative exponents, and transition easily between roots and exponents.

**Lesson: Arithmetic and Geometric Sequences prerequisite for recursive exponential**

A3.2.4 Understand and use the fact that the base of an exponential function determines whether the function increases or decreases
and how base affects the rate of growth or decay.

**Lesson: Recursive Linear Functions**

A2.1.5 Recognize that functions may be defined recursively. Compute values of and graph simple recursively defined functions.

**Lesson: Exponential Recursive Functions (Sets the stage for exponential functions)**

A2.1.5 Recognize that functions may be defined recursively. Compute values of and graph simple recursively defined functions.

**Lesson: Equations to Model Exponential Recursive Calculations (Introduces Exponential Functions)**

A3.2.1 Write the symbolic form and sketch the graph of an exponential function given appropriate information.

**A3.2.4** Understand and use the fact that the base of an exponential function determines whether the function increases or
decreases and how base affects the rate of growth or decay.

**A3.2.5** Relate exponential and functions to real phenomena, including half-life and doubling time.