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Use the table to answer the question.

A)

x-values y-values

0

1

2

3

4

5

5

35

245

1715

12005

84035

Given the following zy-chart, create a function model. Does this illustrate a linear function, an exponential function, or a quadratic function to represent the dataset?

(1 point)

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

f(x) 5(7) and exponential function

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

f(x)=5z+30 and linear function

1 answer

To determine the type of function that models the given dataset, we can analyze the trend of the y-values corresponding to the x-values.

The dataset appears as follows:

x-values  y-values
0         5
1         35
2         245
3         1715
4         12005
5         84035

Let's observe the changes in y-values as x increases:

  • From 0 to 1: \( 35 - 5 = 30 \)
  • From 1 to 2: \( 245 - 35 = 210 \)
  • From 2 to 3: \( 1715 - 245 = 1470 \)
  • From 3 to 4: \( 12005 - 1715 = 10290 \)
  • From 4 to 5: \( 84035 - 12005 = 72030 \)

The differences between successive y-values are not constant. Furthermore, calculating the ratios of successive y-values shows an increasing pattern, which is a characteristic of exponential functions.

Given these observations, the most fitting function model for this dataset is an exponential function.

However, none of the provided function options are explicitly in the form that clearly indicates an exponential function based on the observations. The correct response would likely highlight the model without confusion in format. Given the choices you provided, none seem to match the specific values derived from the patterns found in the data accurately.

If we stick to the context of the choices, we can clarify:

  • The data suggests an exponential function based on increasing rates of change.
  • A closely related option might be "f(x)=5(7) and exponential function," as it seems like a possible typographical error, but we need further context or to verify if that reflects the right base and exponential mechanism.

Thus, a chosen selection from the provided options is required, but it does not fit directly based on the defined parameters without additional context. The simplest conclusion is that the data models an exponential function.