This question is from an exam paper for the Merchant Navy but the questions are similar to those found in A Level Maths so I hope this is in the right place.
- Variables P and V are thought to be related by a law of the form: $PV^n=C$ where n and C are constants.
Observations of P and V are recorded below:
P=15, V=4.42
P=20, V=3.55
P=30, V=2.60
P=40, V=2.06
P=50, V=1.74
Suggested scales: 2cm=0.1 (I've used Desmos to plot the points anyway)
Part (a) Draw a straight line graph to verify this relationship. Part (b) Use the graph drawn in (a) to estimate the values of n and C.
My attempts:
(a) Graph of the plotted points
First of all, this isn't a straight line graph so that's totally thrown me. Even if you plot it on paper you won't get the straight line graph it wants you to get?
(b) I can rearrange $PV^n = C$ to $P=\frac{C}{V^n}$ but not sure how to estimate the values from that or the graph. It's going to be a reciprocal graph, but how do you estimate the values of C or n? My best guess is that n=1 and C=80 using Desmos to plot the graphs.
Any form of guidance is most helpful.