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# Comparing Exponential and Linear Functions

Comparing Exponential and Linear Functions. Lesson 3.2. Table of Values. Use the data matrix of your calculator to enter the following values. Column 1 is the x values Columns 2 and 3 are the f(x) and g(x). Table of Values. Click APPS then 6, then Current (F1, 8 to clear if needed)

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## Comparing Exponential and Linear Functions

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1. Table of Values • Use the data matrix of your calculator to enter the following values. • Column 1 is the x values • Columns 2 and 3 are the f(x) and g(x)

2. Table of Values • Click APPS then 6, then Current(F1, 8 to clear if needed) • Enter values as shown below

3. Two Different Functions • Note the succession of values for f(x) • Differ by 6 each • This implies linear

4. Cursor must be here Note ratio is 1.3 Two Different Functions • Note the succession of values for g(x) • They do NOT differ by a constant • However, the successive values have the same ratio • Show by placing formula in column 4 This shows it is an exponential function.

5. How to Determine the Formula • From previous lesson we know that • Where b is the growth factor • In our case the common ratio = 1.3 • Solve for a • Substitute b = 1.3, any ordered pair

6. Determine Function from Two Points • We can create twoequations with twounknowns • Solve for one of the variables • Substitute into the other equation • (-1, 2.5) (1, 1.6) • Answer b=0.8a=2

7. Lineary = m*x + by = m+m+ … m+ b x terms Exponentialy = a * bxy = a * b * b * … * b x factors Compare and Contrast

8. Compare and Contrast • Exponential growth will always outpace linear growth • In the long run • Eventually • Question:Where? • Solve graphically or algebraically or observe table

9. Where Exponential Passes Linear • Giveny = 100 (1.02)x y = 100 + 12x • Algebraically : no current tools to solve 100 (1.02)x = 100 + 12x • Graphically : ask calculator to find intersection • Or observe tables

10. Assignment • Lesson 3.2A • Page 119 • Exercises3, 5, 7, 9, 11, 13, 15, 17, 21, 23, 25 • Lesson 3.2B • Page 121 • Exercises27 – 39 odd

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