Find the equation of the exponential function represented by the table below.

Question

x      y

 

0      3

1      1.5

2      0.75

3      0.375

Answer 1

The values of y are being cut in half for each increase in x.  This follows the pattern (1/2)^x.  So we're looking at a general function

 

y = C(1/2)^x.  To find C, set x=0:

y = C(1/2)⁰.  When x=0, y=3.  And (1/2)⁰ = 1:

3 = C(1),  or C = 3.

 

The function is 3*(1/2)^x.