1. Compare Linear, Exponential and Quadratic Models
Objective: Students will be comparing linear, exponential and quadratic functions using graphs and tables.

2. Linear Functions Y = 3x + 5 X -1 1 2 Y 5 8 111 2 Y 5 8 11
When the function is linear then there is a constant difference between each of the y values

3. Exponential Functions
Y =0.5(2)x X -1 1 2 Y
0.25
0.5
If you notice the differences are not the same, then try dividing the y values to find a common ratio.

4. Quadratic Functions Y = x2 – 2x + 2 X -1 1 2 3 Y 51 2 3 Y 5
If the differences are not the same. (5 -2 = 3, and 2-1 = 1) And the ratios are not the same ( 2/5 = 0.2 and ½ = 0.5). Then this function is neither linear nor exponential. But if the second differences are the same then the function is quadratic.

5. Using differences and ratios tell whether the values in the table represent a linear, exponential or quadratic function. X 1 2 3 4 Y -1 -2 -3 X -2 -1 1 2 Y -4 X -1 1 2 3 Y 16 4
1/16 X -3 -2 -1 1 Y
13.5 6
1.5

6. Air Temp, A (ºC) 26 27 28 29 30 Body Tem (ºC) 33.44 33.78 34.12 34.46
The table shows the body temperature B (in degrees Celsius) of a desert spiny lizard at various air temperatures A (in degrees Celsius) Tell whether the data can be modeled by a liner function, an exponential function, or a quadratic function.
Air Temp, A (ºC) 26 27 28 29 30
Body Tem (ºC)
33.44
33.78
34.12
34.46
34.80

7. A chambered nautilus is a marine animal that lives in the outermost chamber of its shell. When the Nautilus outgrows a chamber it adds a new, larger chamber to its shell. The table shows the volumes (in cubic cm) of consecutive chambers of a nautilus. Tell whether the data can be modeled by a linear function, an exponential function, or a quadratic function.
Chamber 1 2 3 4 5 6
Volume (cm3)
0.837
0.889
0.945
1.005
1.068
1.135

8. The time it takes for a clock’s pendulum to swing from one side to another and back again is called the pendulums period. The table shows the period t (in seconds) of a pendulum of length l (in feet). Tell whether the data can be modeled by a liner function, and exponential function or a quadratic function.
Period, t(sec) 1 2 3 4 5
Length, l (ft)
0.82
3.28
7.38
13.12
20.5