Section 3.5 - Equation Solving and Modeling

Essential Question(s): 

How are logarithms used with modeling and solving application problems?

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Follow these three steps to complete this "flip" lesson.

STEP 1: Preparation 
Title your spiral with the heading above and copy the essential question(s).

STEP 2: Vocabulary & Examples 
Copy and define the following of vocabulary. This can be any tables, properties, theorems, terms, phrases or postulates listed. Review the following examples and copy what is necessary for you. Use the guiding questions for your cornell notes.

Solving Exponential Equations

• What are the one-to-one properties between exponential and logarithmic functions? (pg 320)
• How do you solve an exponential equation algebraically? (Ex 1 pg 320)
• How do you solve an exponential equation graphically? (Ex 2 pg 321)

Solving Logarithmic Equations

• What must you keep track of when solving logarithmic equations? (pg 321)
• How do you solve a basic logarithmic equation? (Ex 321 & pg 321-322; look at paragraph after)
• How do you solve a logarithmic equation? (Ex 4 pg 321)

Orders of Magnitude and Logarithmic Models

• What is an order of magnitude? (Pg 323)
• How are orders of magnitude used? (Pg 323-324)
• How can you compare Earthquake intensities? (Ex 5 pg 324)
• How can you compare Chemical acidity? (Ex 6 pg 325)

Newton's Law of Cooling

• What is Newton's Law of Cooling? (pg 326)
• How do you apply Newton's Law of Cooling? (Ex 7 pg 326-327)
• What is another form of Newton's Law of Cooling and when it is used? (Pg 327)
• How do you model with Newton's Law of Cooling? (Ex 8 pg 327)

Logarithmic Re-expression

• What are the regression models related by Logarithmic Re-Expression? (pg 328-329)
• How do you use the appropriate regression model? (Ex 9 pg 330)

STEP 3: Reading
Read the following page(s) and take any extra notes as needed.

• Read pages 320 - 330.
• Make sure to read the paragraphs between the examples.