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Tables

Site: Clare-Gladwin RESD
Course: Michigan Algebra I
Book: Tables
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Date: Wednesday, January 15, 2025, 3:34 PM

Description

Tables

Table of contents

Exponential Functions

Exponential functions are written in the form: y = abx, where b is the constant ratio and a is the initial value. By examining a table of ordered pairs, notice that as x increases by a constant value, the value of y increases by a common ratio. This is characteristic of all exponential functions.

In the table below notice that as the x-values increase by 1, the y-values double. In other words, to get from one y-value to the next, multiply by 2, therefore the common ratio is 2.

TableExpFunc1

To find the equation that represents this table of values, substitute any ordered pair from the table into the equation, and solve for a.
TableExpFunc2

So the model for this data is: TableExpFunc3

Example 1

Find an exponential model for the table below.

TableEx1-1

Step 1. Find the common ratio for the table.

TableEx1-2
Step 2. Use an ordered pair to solve for the value of a.

TableEx1-3

Step 3. Use the values of a and b to write an equation.

Example 2

Write an exponential model for the table below.
TableEx2-1

Step 1. Fill in the table to include the missing values for x.

Example 2 Continued

Step 2. Find the value for b.
TableEx2-3

Since each value of y is moved 2 units for x, TableEx2-4, or b2 is required to move between two points. To determine the b -value, set up an equation and solve.

10•b2 = 250

b 2 = 25

b = 5

Step 3. Use an ordered pair to solve for the value of a.

For this example, use the point (1, 10)

TableEx2-5

Step 4. Use the values of a and b to write an equation.

Video Lesson

To learn how to find models of exponential functions select the following link:

Modeling Exponential Functions #1

Guided Practice

To solidify your understanding of writing exponential models, visit the following link to Holt, Rinehart and Winston Homework Help Online. It provides examples, video tutorials and interactive practice with answers available. The Practice and Problem Solving section has two parts. The first part offers practice with a complete video explanation for the type of problem with just a click of the video icon. The second part offers practice with the solution for each problem only a click of the light bulb away.

Guided Practice

Practice

Exponential Models Worksheet

Light Intensity Worksheet
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Answer Keys

Exponential Models Answer Key

Light Intensity Answer Key
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Sources

Castellon, Carol. "Math 117 Lecture 9 notes."

http://www.math.uiuc.edu/~castelln/M117/lecture9_math117.pdf (accessed September 13, 2010).

Embracing Mathematics, Assessment & Technology in High Schools; A Michigan Mathematics & Science Partnership Grant Project

Holt, Rinehart, & Winston. "Exonential and Logarithmic Functions."

http://my.hrw.com/math06_07/nsmedia/homework_help/alg2/alg2_ch07_08_homeworkhelp.html (accessed September 13, 2010).