Hello i have a maths problem i am trying to solve. I have nearly completed it. I am just stuck on the last bit, and looking for some help.
My Question:
Two quantities Q and H are believed to be related by the equation $Q= kH^n$.
The values obtained for Q and H shown in the table below were obtained during an experiment.
Q
0.16
0.20
0.27
0.34
0.40
0.47
0.55
H
1.14
1.78
3.24
5.14
7.11
9.82
13.44
Plotting the values of Q and H using graph paper or computer graphing software show the relationship between Q and H and determine;
a. the gradient of the curve from your graph,
b. the law connecting Q and H, expressing the law that you have determined in the form of an equation.
So far i have drawn the graph and plotted all the points. I got the points like this:
$Q = KH^n$
$Y = ax^n$
$Log (y) = Log (ax)$
$Log (y) = Log (a) + Log(xn)$
$Log (y) = Log (a) + nLog (x)$
$Log (y) = Log (a) + nLog (x)$
[ y ] [ c ] [ x ]
1: Log (0.16) = -0.796
Log (1.14) = 0.0569
2: Log (0.20) = -0.699
Log (1.78) = 0.250
ETC..
I am now stuck on finding the graidient, and connection law. I know n is the graidient, just not how to find it.
Is the connecting law Logarithms?
Any help much appreciated, been stuck on this for a long time.
On a bilogarithmic plot, you expect a straight line,
$$\log Q=n\log H+\log k.$$ This is indeed what you observe.
As the alignment is excellent, you can simply use the two extreme points.
Then
$$n=\frac{\log Q_7-\log Q_1}{\log H_7-\log H_1}$$ and $\log k$ follows.