Use the table to answer the question.

Question

The sequences for the two functions is shown in the table. Which of the following statements are true?

(1 point)
Responses

None of the above
None of the above

While the growth rate of g(x) is initially greater that the growth rate of f(x), the growth rate of f(x) keeps increasing and eventually surpasses the growth rate of g(x).
While the growth rate of g(x) is initially greater that the growth rate of f(x), the growth rate of f(x) keeps increasing and eventually surpasses the growth rate of g(x).

The growth rate of g(x) is initially greater than the growth rate of f(x) between the second and the fifth term.
The growth rate of g(x) is initially greater than the growth rate of f(x) between the second and the fifth term.

While the growth rate of f(x) is initially greater than the growth rate of g(x), the growth rate of g(x) keeps increasing and eventually surpasses the growth rate of f(x).

Answer 1

Without the specific values from the table, I can’t analyze the growth rates of the functions \(f(x)\) and \(g(x)\). However, I can guide you on how to assess the statements based on the table data.

1. Compare Initial Growth Rates: Look at the values of \(f(x)\) and \(g(x)\) at the start, particularly between the second and fifth terms. Determine which function has a higher value and at what point.

2. Evaluate Growth Trends: Calculate the growth rates by finding the differences between consecutive terms for both functions. This will allow you to see if one function's growth rate is consistently higher than the other over the given range.

3. Identify Changes: Observe whether \(f(x)\) eventually starts to grow faster than \(g(x)\), or vice versa. This will help you confirm if one function eventually surpasses the other in terms of growth rate.

4. Determine True Statements: Use the findings from your analysis of initial values and growth trends to determine which of the provided statements are true.

If you can provide the specific values or data from the table, I can help you analyze the information more directly!