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You can use these printouts of the equations, the graphs without axes , the graphs with axes and the processes to create a card sorting activity.
Scientific processes involving two variables can often be represented using equations and line graphs.
In this problem, $9$ processes, their equations and graphs have been mixed up and shown below. In each case, the two variables are represented by the letters $x$ and $y$ and the labels from the axes of the graphs have been removed.
Which can you match up? What is the interpretation of the variables $x$ and $y$ in each case?
Can you identify the physical interpretation of three key points on each of the graphs?
Processes
Line Graphs
Equations
A: $y(x) = 4.9 x^2$
B: $y(x) =500 \times 2^{-0.6667x}$
C: $y(x) =1- 0.01671\cos(0.0172 x)$
D: $y(x) = 12+10\sin(0.121 x)$
E: $y(x) = 5\cos(3.13 x)e^{-0.05x}$
F: $y(x) = \dfrac{11.3 x}{2.1+x}$
G: $y(x) =10 \times 2^{4x}$
H: $y(x) = \dfrac{1000000}{10+(100000-10)2^{-4x}}$
I: $y(x)x = 22.4133$
The numbers have been carefully chosen to represent certain time/length/unit scales for particular physical phenomena. Can you deduce the reason for the choice of any of the numbers?