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Comparing Exponential and Linear Functions Lesson 3.2

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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) x01234567 f(x)1218243036424856 g(x)1215.620.326.434.344.657.975.3

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

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

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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 Cursor must be here Note ratio is 1.3 This shows it is an exponential function.

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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

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

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Compare and Contrast Linear y = m*x + b y = m+m+ … m+ b x terms Exponential y = a * b x y = a * b * b * … * b x factors

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

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Where Exponential Passes Linear Given y = 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

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Assignment Lesson 3.2A Page 119 Exercises 3, 5, 7, 9, 11, 13, 15, 17, 21, 23, 25 Lesson 3.2B Page 121 Exercises 27 – 39 odd

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