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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)

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) class=

Verified Answer :

kudzordzifrancis

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:

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 \(f(x) = 3( {2}^{x} )\).

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