# Comparing Exponential and Linear Functions Lesson 3.2.

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

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

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

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.

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

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

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

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

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

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