Question

Use the table to answer the question.

This table displays the corresponding y-values for a given set of x-values.
x-values y-values
−1
3
0 6
1 12
2 24
3 48
Create an exponential model of the dataset shown in the xy
-chart.

(1 point)
Responses

f(x)=6(2)x
f left parenthesis x right parenthesis equals 6 left parenthesis 2 right parenthesis superscript x baseline

f(x)=12x
f left parenthesis x right parenthesis equals 12 superscript x baseline

f(x)=2(6)x
f left parenthesis x right parenthesis equals 2 left parenthesis 6 right parenthesis superscript x baseline

f(x)=6(2x)

Answer 1

To create an exponential model from the dataset provided, we can observe the pattern in the y-values as the x-values increase.

The x-values and corresponding y-values given are:
- For \( x = 0 \), \( y = 6 \)
- For \( x = 1 \), \( y = 12 \)
- For \( x = 2 \), \( y = 24 \)
- For \( x = 3 \), \( y = 48 \)

Notice that:
- From \( y = 6 \) to \( y = 12 \): \( 12 = 6 \times 2 \)
- From \( y = 12 \) to \( y = 24 \): \( 24 = 12 \times 2 \)
- From \( y = 24 \) to \( y = 48 \): \( 48 = 24 \times 2 \)

This reveals that each y-value is multiplied by 2 as x increases by 1. Therefore, it appears that the function can be of the form \( f(x) = a \cdot 2^x \).

Given that when \( x = 0 \), \( f(0) = 6 \), we can deduce:

\[
f(0) = a \cdot 2^0 = a = 6
\]

Thus the exponential model can be written as:

\[
f(x) = 6 \cdot 2^x
\]

Therefore, the correct answer is:

**f(x) = 6(2^x)**