Question

Use the table to answer the question.

x-values y-values
0 5
1 35
2 245
3 1715
4 12005
5 84035
Given the following xy
-chart, create a function model. Does this illustrate a linear function, an exponential function, or a quadratic function to represent the dataset?

(1 point)
Responses

f(x)=5x+30
and linear function
f left parenthesis x right parenthesis equals 5 x plus 30 and linear function

f(x)=5(7)x
and exponential function
f left parenthesis x right parenthesis equals 5 left parenthesis 7 right parenthesis superscript x baseline and exponential function

f(x)=5(7)x
and quadratic function
f left parenthesis x right parenthesis equals 5 left parenthesis 7 right parenthesis superscript x baseline and quadratic function

f(x)=7(5)x
and exponential function

Answer 1

To determine the type of function that best models the given dataset, we can analyze the growth of the y-values in relation to the x-values.

The given y-values are:

- For x = 0, y = 5
- For x = 1, y = 35
- For x = 2, y = 245
- For x = 3, y = 1715
- For x = 4, y = 12005
- For x = 5, y = 84035

### Step 1: Analyze the Ratio of Consecutive Values

One way to check if a function is exponential is to compute the ratio of consecutive y-values:

- \( \frac{y_1}{y_0} = \frac{35}{5} = 7 \)
- \( \frac{y_2}{y_1} = \frac{245}{35} = 7 \)
- \( \frac{y_3}{y_2} = \frac{1715}{245} = 7 \)
- \( \frac{y_4}{y_3} = \frac{12005}{1715} = 7 \)
- \( \frac{y_5}{y_4} = \frac{84035}{12005} = 7 \)

Since the ratio of consecutive y-values is constant (7), this indicates that the function is exponential.

### Step 2: Formulate the Function

From the analysis, we can model the function as:
\[ f(x) = 5 \times 7^x \]

### Conclusion

Based on this analysis, the correct function model for the dataset is:
**f(x) = 5(7^x) and exponential function.**

So the response would be:
**f(x) = 5(7)^x and exponential function.**