Is the sequence 2 4 8 16 32 a linear function?

NO!!! It is an exponential function.

2 = 2^(1)

4 = 2^(2)

8 = 2^(3)

16 = 2^(4)

32 = 2^(5)

...

2^(n)

If n = x on the co-ordinate axes, that is you go along 1,2,3,4,5 etc., the 'y' values (2,4,8,16,32, etc.,) , do NOT go up in a straight line, but an ever steepening gradient. Hence it is NOT a linear function.