How do you describe the transformation in #y=2^(x-3)#?

Question

2240 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-06-24T12:17:54

The form is # y=a b^x#, with #a = 1/8 and b = 2. The plot of {(x, Y)}, with Y = log y, on a semi-log graph paper will be a straight line,.

This is an exponential transformation, of the form #y=a b^x#.

A short Table for making the graph for

#y=2^(x-3)=(1/8)(2^x)#

is given below.

#(x, y): ... (-4,1/128) (-3, 1/64) (-2, 1/32) (-1, 1/16)#

#(0, 1/8) (1, 1/4) (2, 1/2) (3, 1) (4, 2)....(N, 2^(N-3)) ...#

Equating logarithms, #Y=log y =x log 2 - 3 log 2#

The plot of [{x, Y)}, with Y= log y, on a semi-log graph paper, will be a

straight line.