Question

A 2-column table has 5 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1, 2. The second column is labeled f (x) with entries 16, 8, 4, 2, 1. Which exponential function is represented by the values in the table?

Answer 1

Answer:

It is an exponential function with base 1/2 and exponent x - 2.

Step-by-step explanation:

Hope it was helpful..

Answer 2

Given:

x:    -2   -1     0   1   2

f(x):  16   8    4    2  1

To find:

Exponential which represents the values in the given table

Solution:

Let exponential function

$f(x)=a^{x+c}$

where  c is constant.

Substitute x=0

$f(0)=a^{c}$

$a^{c}=4$

$f(1)=a^{1+c}$

$a^{1+c}=2$

$\frac{a^c}{a^{1+c}}=2$

$\frac{1}{a}=2$

$a=\frac{1}{2}$

$4=(\frac{1}{2})^{c}$

$2^{2}=2^{-c}$

By comparing we get

-c=2

$\implies c=-2$

Now, the exponential function

$f(x)=(\frac{1}{2})^{x-2}$