Question

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

x y
(0,2)
(1,4)
(2,8)
(3,16)

Answer 1

y = 2
`(2)^(x)`

Explanation:

For the exponential function in the form

y = a
`(b)^(x)`

Use the ordered pairs from the table to find a and b

Using (0, 2 ) , then

2 = a
`b^(0)` (
`b^(0)` = 1 ) , thus

a = 2 , so

y = 2
`b^(x)`

Using (1, 4 ) , then

4 = 2b ( divide both sides by 2 ) , then

b = 2

Thus exponential function is

y = 2
`(2)^(x)`