Rishik K started from the eight processes, and matched each one to an equation and type of graph. In some cases, Rishik also suggested what the numbers A, B and C could be. Here is Rishik's work:

1. A cup of tea is made and the temperature measured in degrees Celsius every second. What would the temperature - time graph look like?
   $$y = \frac{A}{e^x}+B$$
   
    
2. The height of the valve on a bicycle tyre above the ground is measured after each centimetre that the bicycle travels forwards. What would the height - distance graph look like?
   $$y=A\sin {Bx} +A$$
   
   A=12
   
   If $A=12$ then the highest point above the ground that the valve reaches is 24 centimetres. That means the bicycle has very small wheels!
    
3. I throw a tennis ball straight up into the air and catch it. The height of the ball from the ground is measured over the time of the journey using freeze-frame photography. What would the height - time graph look like?
   $$y=Ax^2$$
   
   A has to be a negative number.
    
4. I measure several objects using inches and then using metres, plot them on a scatter graph, and join the points. What would the metres - inches graph look like? 
   $$y=Ax$$
   
   A definitely has to be more than 0.
    
5. I jump out of a plane and the distance fallen from the plane is measured every $0.1$ second until I open my parachute. What would the distance fallen - time graph look like whilst in freefall?
   $$y=Ax^2+Bx+C$$
   
   A must be more than 0. If A was negative, it would instead be an upside-down parabola. I think B and C may be 0.
    
6. I drive at 70 miles an hour along the motorway and note the reading on my odometer (mile counter) every 5 minutes. What would the odometer reading - time graph look like? 
   $$y=Ax+B$$
   
   A is an incredibly small positive fraction and B is 1 because the line has a y intercept at (0,1)
   
   It looks like this conclusion comes from looking at the graph - but it's important to think about the real-life process as well, especially since we don't know the scale on the graph. Is it possible that the graph here could be swapped with the graph for process 4 (measuring objects in inches and in metres)?
    
7. I blow up a roughly spherical balloon using a balloon pump. After each pump I measure the radius of the balloon in centimetres. What would the radius - number of pumps graph look like?
   $$y=\sqrt[3]{x}$$
   
    
8. I suck water through a straw out of a large beaker at a constant rate and measure the volume of liquid remaining at various times. What would the volume-time graph look like?
   $$y=Ax+B$$
   
   A is negative and B is 5 because the line crosses the y axis at (0,5).
   
   Again, remember that the graph scale is not given, so the value of the intercept cannot be read from the graph.We also do not know which line represents the x- or y- axis.