Question 145939
<pre><font size = 4 color = "indigo"><b>
plot the points: (1,1), (2,2),(3,4),(4,8),(5,16)

{{{drawing(160,400,-2,6,-2,18,graph(160,400,-2,6,-2,18), 
locate(1-.2,1+.45,"o(1,1)"),   
locate(2-.2,2+.45,"o(2,2)"), 
locate(3-.2,4+.45,"o(3,4)"), 
locate(4-.2,8+.45,"o(4,8)"), 
locate(5-.2,16+.45,"o"),
locate(2.2,16+.45,"(5,16)")

 ) }}}

Connect each pair of successive points:

{{{drawing(160,400,-2,6,-2,18,graph(160,400,-2,6,-2,18), 
locate(1-.2,1+.45,o),   
locate(2-.2,2+.45,o), 
locate(3-.2,4+.45,o), 
locate(4-.2,8+.45,o), 
locate(5-.2,16+.45,o),line(1,1,2,2),line(2,2,3,4),line(3,4,4,8),line(4,8,5,16)
 ) }}}

Draw a rise and a run between each successive
pair of points:

{{{drawing(160,400,-2,6,-2,18,graph(160,400,-2,6,-2,18), 
locate(1-.2,1+.45,o),   
locate(2-.2,2+.45,o), 
locate(3-.2,4+.45,o), 
locate(4-.2,8+.45,o), 
locate(5-.2,16+.45,o),
triangle(1,1,2,2,2,1),
triangle(2,2,3,4,3,2),
triangle(3,4,4,8,4,4),
triangle(4,8,5,16,5,8)
 ) }}}

In going from the point (1,1) to the point (2,2)
the rise is 1 and the run is 1, so the rate of change
in going from the point (1,1) to the point (2,2)
is  1 y-unit per 1 x-unit.

In going from the point (2,2) to the point (3,4)
the rise is 2 and the run is 1, so the rate of change
in going from the point (2,2) to the point (3,4)
is  2 y-units per 1 x-unit. 

In going from the point (3,4) to the point (4,8)
the rise is 4 and the run is 1, so the rate of change
in going from the point (3,4) to the point (4,8)
is  4 y-units per 1 x-unit.

In going from the point (4,8) to the point (5,16)
the rise is 8 and the run is 1, so the rate of change
in going from the point (4,8) to the point (5,16)
is  8 y-units per 1 x-unit.

So the rate of change between successive points 
doubles each time.

Edwin</pre>