Question

Which exponential function is represented by the values in the table?


f(x) = 3(2x)

f(x) = 2(2x)

f(x) = 3(3x)

f(x) = 2(3x)

Answer 1

ANSWER

The exponential function is
$f(x) = 3( {2}^{x} )$

EXPLANATION

Let the exponential function that is represented by the values in the table be of the form,

$f(x) = a( {b}^{x} )$

The points in the table must satisfy this exponential function.


We substitute the point,

$(0,3)$

to get,


$3 = a( {b}^{0} )$



This implies that,


$3 = a( 1 )$


$3 = a$


Our function now becomes,

$f(x) = 3( {b}^{x} )$


We gain, plug in another point yo find the value of b too.


Let us substitute
$(1,6)$


This implies that,

$6= 3( {b}^{1} )$


We divide through by 3 to obtain,

$2 = b$


Therefore the function is,


$f(x) = 3( {2}^{x} )$



The correct answer is A.

Answer 2

Answer:

The function $f(x) = 3( {2}^{x} )$.

Step-by-step explanation:

Given : Table for x and f(x).

To find : Which exponential function is represented by the values in the table.

Solution :  Let the exponential function that is represented by the values in the table be of the form,

$f(x) = a( {b}^{x} )$

On plugging the values from table (0,3)

$3 = a( {b}^{0} )$ we get ,

3 = a.

tex]f(x) = 3( {b}^{x} )[/tex]

To find value of b we substituting other point from table (1,6)

tex]6 = 3( {b}^{1} )[/tex].

2 = b.

Therefore , the function $f(x) = 3( {2}^{x} )$.