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) x 1 2 3 4 5 6 7 f(x) 12 18 24 30 36 42 48 54 g(x) 15.6 20.3 26.4 34.3 44.6 57.9 75.3

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

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 * bx 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 3.2 Page 119 Exercises 1 – 41 odd