Lesson 1.1.2 Rational and Irrational Numbers and Their Properties

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By the end of this lesson, I will be able to answer the following questions…

1. How can I solve a basic exponential equation?

2. How can you determine the whether the sum or product of two numbers will be rational or irrational AND determine closure?

3. Can I apply properties of exponent to solve solve growth and decay scenarios?

Vocabulary• Exponential Equation

• Closed Operations – The sum of two rational numbers is a rational number. – The product of two rational numbers is a rational number. – The sum of a rational number and an irrational number is anirrational number. – The product of a rational numberand an irrational number is an irrational number.

Prerequisite Skills with Practice

Rewrite the following without exponents.

Example one

Simplify the expression

GeoGebra Example One

Example two

Simplify the expression

GeoGebra Example Two

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Example three

A wealthy hamster has a savings account. The totalbalance, y, after any number of years t can be found using the equation

where x is 1 plus the annualinterest rate. The balance in the account is currently$6203.74 and the hamster hashad the account for years.

What is the annual interest rate?

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Example four

Solve the equation