1. Comparing Linear and Exponential Models

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

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

4. YOU DO: use the differences and ratios to determine if the function is linear or exponential1 2 3 4 Y -1 -2 -3
Same Constant Difference Or
Same Constant Ratio X -1 1 2 3 Y 16 4
1/16
Same Constant Difference Or
Same Constant Ratio

5. 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 neither
Air Temp, A (ºC) 26 27 28 29 30
Body Tem (ºC)
33.44
33.78
34.12
34.46
34.80
Linear

6. 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 neither
Chamber 1 2 3 4 5 6
Volume (cm3)
0.837
0.889
0.945
1.005
1.068
1.135
Exponential

7. Identifying continuous and discrete data and functions
Data that has specific interval values are considered discrete data.
Domain and Range are in set notation
Example:
Die Roll:
S = {1,2,3,4,5,6}
A Data that is not at specific intervals is called continuous data.
Domain and Range are in interval notation
Example:
Height of a blue bird (inches):
S = [0, 6]