Non-linear Graph Questions
You will need to have read your notes on these ideas first!
1. As electrical signals pass through a cable their intensity is attenuated (reduced). A student
measures the intensity in volts of the signal at different distances along a cable and obtains
the following results:
Intensity, I (V)
Distance, x (m)
74.1
1
54.9
2
40.7
3
30.1
4
22.3
5
16.5
6
12.2
7
9.1
8
The student then does some research and discovers this formula:
I = I0 exp-μx
Where μ is the coefficient of attenuation. The students decides it would be of interest to find
out what μ is for the material the cable is made from.
(a) Use your knowledge of natural logs to process and re-arrange the formula above so it is of
the form y=mx +c
(b) It should then be clear that you need to find the natural log of one of the quantities in the
table. Use the spare column to do this and label the column.
(c) Plot an appropriate log-linear graph.
(d) From the graph determine μ and I0 (the intensity of the signal before it has passed through
any cable).
2. Another student investigates the relationship between velocity and kinetic energy for an
object of mass 100 kg.
(a) What formula relates these quantities?
(b) Use your knowledge of logs (base10) to process and re-arrange the formula to be of the
form y=mx + c
(c) The student collects results as shown:
Kinetic Energy (J) Velocity, v (m s-1)
1250
5.0
5000
10.0
11250
15.0
20000
20.0
31250
25.0
45000
30.0
Process the results, record them in the blank columns of the table, and plot an appropriate
log-log graph.
(d) Use your graph to check that the object is behaving as you would expect according to the
formula. Explain how you can tell whether it is or it isn’t.