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Title: van der waals
Description: These notes served as our performance task last semester. This function is based on the van der Waals equation for predicting the pressure p of a gas as a function of v at a fixed temperature.
Description: These notes served as our performance task last semester. This function is based on the van der Waals equation for predicting the pressure p of a gas as a function of v at a fixed temperature.
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Given problem: Consider the rational function π =
512500v2 β449000v+19307
125vΒ²(1000vβ43)
...
The function above models
the pressure p of a carbon dioxide in terms of volume v if the temperature is 500
Kelvins
...
Sketch the graph of the function
...
What is the domain of the function? (1 point)
Denominator of the function: 125v2(1000v-43)=0
125v2
1000v-43
ππππΒ²
π
1000π£ β 43 = 0
=
1000π£ = 43
πππ
πππ
1000π£
43
π= π
=
1000
1000
43
π£=
ππ 0
...
What is/are the vertical asymptote(s) of the function? (1 point)
125v2(1000v-43)=0
ππππΒ²
π
=
πππ
πππ
π= π
πππππ β ππ = π
πππππ = ππ
πππππ
ππ
=
ππππ
ππππ
ππ
π=
ππ π
...
What is the horizontal asymptote of the function? (1 point)
Note: If the denominatorβs degree is greater than the numeratorβs degree, the
horizontal asymptote is the x-axis (v); y=0 (p)
Denominatorβs degree= 3
Numeratorβs degree= 2
Therefore, the horizontal
asymptote is p=0
5
...
6
...
7
...
(5 points)
INTERVAL
π<0
Test Point
512500π£ 2 β 449000π£ + 19307
125π£ 2 (1000π£ β 43)
512500v 2 β 449000v + 19307
π=
125vΒ²(1000v β 43)
-1
+
-
π< π£<
ππ
ππππ
or 0
...
040
+
-
ππ
ππππ
0
...
Explain the significance of the vertical asymptote(s) in practical terms
...
043 liters
...
9
...
(5 points)
As the volume increases, the pressure becomes closer to 0
...
Title: van der waals
Description: These notes served as our performance task last semester. This function is based on the van der Waals equation for predicting the pressure p of a gas as a function of v at a fixed temperature.
Description: These notes served as our performance task last semester. This function is based on the van der Waals equation for predicting the pressure p of a gas as a function of v at a fixed temperature.