Use the table to answer the question.

Question

x f(x)=a⋅bx
x0 a⋅bx0
x0+Δx a⋅b(x0+Δx)
x0+2Δx a⋅b(x0+2Δx)
Ramona wants to use the table to prove something about how exponential functions grow. What does she need to do next and what will she be able to prove?

(1 point)
Responses

Ramona needs to subtract the x-values from the f(x)-values. She will be able to prove that exponential functions grow by equal differences over equal intervals.
Ramona needs to subtract the x -values from the f left parenthesis x right parenthesis -values. She will be able to prove that exponential functions grow by equal differences over equal intervals.

Ramona needs to subtract the x-values from the f(x)-values. She will be able to prove that exponential functions grow by equal factors over equal intervals.
Ramona needs to subtract the x -values from the f left parenthesis x right parenthesis -values. She will be able to prove that exponential functions grow by equal factors over equal intervals.

Ramona needs to add another column to the table and find the change in f(x)-values. She will be able to prove that exponential functions grow by equal differences over equal intervals.
Ramona needs to add another column to the table and find the change in f left parenthesis x right parenthesis -values. She will be able to prove that exponential functions grow by equal differences over equal intervals.

Ramona needs to add another column to the table and find the growth factors between the consecutive values of f(x). She will be able to prove that exponential functions grow by equal factors over equal intervals.
Ramona needs to add another column to the table and find the growth factors between the consecutive values of f left parenthesis x right parenthesis . She will be able to prove that exponential functions grow by equal factors over equal intervals.
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Answer 1

To explore the growth characteristics of an exponential function using the given table, Ramona needs to find the growth factors between the consecutive values of \( f(x) \). This involves adding another column to the table that calculates the ratio of consecutive \( f(x) \) values, which will help her illustrate that the growth of the function occurs by equal factors over equal intervals.

Therefore, the correct response is:

Ramona needs to add another column to the table and find the growth factors between the consecutive values of \( f(x) \). She will be able to prove that exponential functions grow by equal factors over equal intervals.