To analyze the dataset provided, we can look at the values of \( y \) for each corresponding \( x \):
- \( x = 0 \), \( y = 5 \)
- \( x = 1 \), \( y = 35 \)
- \( x = 2 \), \( y = 245 \)
- \( x = 3 \), \( y = 1715 \)
- \( x = 4 \), \( y = 12005 \)
- \( x = 5 \), \( y = 84035 \)
First, let's observe how the values of \( y \) change with respect to \( x \).
Change in \( y \) Values
To understand whether the function is linear, exponential, or quadratic, we can look at the ratios of successive \( y \) values.
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From \( x = 0 \) to \( x = 1 \): \[ \frac{35}{5} = 7 \]
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From \( x = 1 \) to \( x = 2 \): \[ \frac{245}{35} = 7 \]
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From \( x = 2 \) to \( x = 3 \): \[ \frac{1715}{245} = 7 \]
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From \( x = 3 \) to \( x = 4 \): \[ \frac{12005}{1715} = 7 \]
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From \( x = 4 \) to \( x = 5 \): \[ \frac{84035}{12005} = 7 \]
Each ratio is constant (7), which indicates that the function is exponential.
Conclusion
This dataset can be modeled by an exponential function of the form: \[ f(x) = 5(7^x) \] Thus, the best fit for the function based on the given options clearly shows that this is an exponential function.
Final Answer
The function model is \( f(x) = 5(7^x) \) and it represents an exponential function.