algebra ii chapter 7: exponential and part...

Alg II Chapter 7 Notes Part 2.notebook

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January 21, 2015

Algebra IIChapter 7:

Exponential and Logarithmic

Functions Part 2

Chapter 7 Lesson 4Evaluate Logarithms and Graph Logarithmic Functions

Vocabulary


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Example 1: Rewrite Logarithmic Equations

Example 2: Evaluate Logarithms Helpful examples:

= x

= x


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Example 3: Evaluate Common and Natural Logarithms

When this is no subscript number but it still says log, the number is 10! It is a common logarithm problem!

When this is no subscript number and the log changes to ln, the number is e! It is a natural log problem!

Round to three decimal places!

Example 4: Evaluate a Logarithmic Model


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Example 5: Use Inverse Properties What happens with inverse functions?

When you substitute one into the other, the value is x!!!

Example:Simplified:

Example 6: Find Inverse Functions Reminder for Solving for Inverse:1. Write the original function in terms of x and y.2. Switch x and y.3. Solve for y.


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Example 7: Graph Logarithmic Functions

1. Write in exponent form.2. Make a table of values. You choose the RANGE because it will be more convenient! 3. Check the base to figure out if the graph is the inverse of a growth or decay function.4. Plot the points and identify any asymptotes.5. Using the asymptote to begin with, draw a smooth curve through the points.

Notice:These are inverse functions of the growth and decay functions!

Identify b, h, and k any asymptotes and if this is inverse of growth or decay.

Example 8: Translate a Logarithmic Graph

1. Ignore the h and k for now. You will graph the parent function in exponent form first.2. Make a table of values. Choose convenient values. 3. Check the base to figure out the asymptote of the parent.4. Using the asymptote to begin with, draw a smooth curve through the points to graph the parent function.5. Use the h and k to translate the original points. (horizontal(h) and vertical(k). Figure out the new asymptote. (Since it is the inverse of an exponential function, it now involves the h!!!)6. Using the new asymptote, draw a smooth curve through the new points.

Identify b, h, and k any asymptotes and if this is inverse of growth or decay.


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Chapter 7 Lesson 5Apply Properties of LogarithmsVocabulary

Words to Review:

Base

Example 1: Use Properties of Logarithms


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Example 2: Expand a Logarithmic Expression

Example 3: Standardized Test Practice


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Example 4:

Example 5: Use Properties of Logarithms in Real Life


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Chapter 7 Lesson 6Solve Exponential and Logarithmic Equations Vocabulary

Example 1: Solve by Equating Exponents

Check to see if you can somehow make the bases the same. Always check your solutions! In some cases, there will be extraneous solutions!


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Example 2: Take a Logarithm of Each Side

It is allowed to "take the log of each side". According to the inverse statement above, if you take the log with the same base as the current base, you will be left with only the exponent!

Example 3: Use an Exponential Model

T = Temperature after time

T = Initial Temperature

T = Surrounding Temperature

r = rate of cooling

t = time (in minutes)

O

R


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Example 4: Solve a Logarithmic Equation

Example 6: Standardized Test Practice Try to take the log of a negative number on your calculator. What happens and why?


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Example 5: Exponentiate Each Side of an Equation

It is allowed to "make each side an exponent of the same base". According to the inverse statement above, if you make each side an exponent of the same base that is the current log base, the base and the log will cancel.

Example 7: Use a Logarithmic Model


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January 21, 2015

Chapter 7 Lesson 7Write and Apply Exponential and Power FunctionsVocabulary

Words to Review:

Power Function

Exponential Function

Example 1: Write an Exponential Function 1. Create two equations by substituting coordinates of the two points into .2. Solve for a in the first equation.3. Substitute the a value from step 2 into the second expression for a. This will allow you to find b. Reminder: b>0!4. Find a by substituting the b value back into the first equation.5. Rewrite the equation with the new a and b values using .


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Example 2: Find an Exponential Model

Example 3: Use Exponential Regression

Use your calculator to find an exponential regression.1. Enter the lists OF THE ORIGINAL DATA!!!2. Touch "STAT".3. Scroll over to "CALC".4. Scroll to 0:ExpReg. Select it.5. Touch "ENTER".

Equation given by calculator:

Now graph it to find out how many scooters sold in the 8th year:


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Example 4: Write a Power Function 1. Create two equations by substituting coordinates of the two points into .2. Solve for a in the first equation.3. Substitute the a value from step 2 into the second expression for a. This will allow you to find b. Reminder: b>0!4. Find a by substituting the b value back into the first equation.5. Rewrite the equation with the new a and b values using .

Example 5: Find a Power Model


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Example 6: Use Power Regression

Use your calculator to find an exponential regression.1. Enter the lists OF THE ORIGINAL DATA!!!2. Touch "STAT".3. Scroll over to "CALC".4. Scroll to A:PwrReg. Select it.5. Touch "ENTER".

Equation given by calculator:

Now graph it to find out how many scooters sold in the 8th year:

algebra ii chapter 7: exponential and part...

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