This table displays the corresponding y-values for a given set of x-values.

Question

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

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

f(x)=12^x

Answer 1

To create an exponential model for the given dataset, we need to identify the pattern in the y-values corresponding to the x-values.

Let's analyze the y-values:

• When \( x = 0 \), \( y = 6 \)
• When \( x = 1 \), \( y = 12 \)
• When \( x = 2 \), \( y = 24 \)
• When \( x = 3 \), \( y = 48 \)

We can see that as \( x \) increases by 1, \( y \) doubles:

• From \( 6 \) to \( 12 \) (doubles)
• From \( 12 \) to \( 24 \) (doubles)
• From \( 24 \) to \( 48 \) (doubles)

This indicates that the relationship can be modeled by an exponential function of the form:

\[ f(x) = a \cdot b^x \]

From the data, we see that when \( x = 0 \), \( f(0) = 6 \), thus:

\[ a = 6 \]

The doubling happens for each increment of \( x \), which means \( b = 2 \).

Thus, we can write the function as:

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

Therefore, the correct exponential model is:

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

So the response is:

f(x) = 6(2)^x