EasyMathematicsHigh School (11–12)Functions and Calculus › Functions as Models of DataNumericalBoard Exam
A fixed amount of gas at a fixed temperature has a volume of 8 L at a pressure of 120 kPa…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A fixed amount of gas at a fixed temperature has a volume of at a pressure of . The product stays constant. Write the volume as a function of the pressure, and find the volume at .
Need a reminder? The key ideaShow
Choose the family from the data: a straight line for equal steps, a parabola for a square law, a reciprocal for a constant product. Trust a model inside the range of its data, not far outside it.
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. The constant. .
Step 2. The model. .
Step 3. At . .
Answer: ; at .
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