Name _______________________________________
Asymptotic Behavior of Functions
pH of Acid-Base Solutions
Data Collection
pH of household ammonia
pH of vinegar
Initial volume of vinegar
__________
__________
__________ ml
Added volume of
ammonia (ml)
Total volume of
ammonia (ml)
pH
0
2
2
1
1
2
4
0
2
4
5
6
8
12
Added volume of
ammonia (ml)
Total volume of
ammonia (ml)
pH
4
4
8
8
20
20
124
16
20
28
36
56
76
200
Data Analysis
Create the graph of pH as a function of ammonia volume.
On the graph of pH as a function of volume, draw a horizontal asymptote for this function and
write its equation.
Explain why you have chosen this equation for the horizontal asymptote.
Explain why the pH function has a horizontal asymptote.
Analyze the boundaries of the pH function when the volume of ammonia is approaching infinity
(end behavior as x approaches infinity). Determine the range of this function.
If you were to model this experiment with a function, what type would it be?
Further Exploration
Consider a situation where acid is added to base. Then the pH values approach a horizontal
asymptote from larger values and the pH function is bounded from below. Draw this function.
Connecting Mathematics with Science: Experiments for Precalculus