SOLUTION: Please help me Evaluate the functions for the values of x given as 1, 2, 4, 8, and 16. Describe the differences in the rate at which each function changes with increasing values of

plot the points: (1,1), (2,2),(3,4),(4,8),(5,16)



Connect each pair of successive points:



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



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