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?

Question

A. 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.

B. 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.

C. 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.

Answer 1

The correct choice is:

B. 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.

This approach will show that for each equal interval of \(x\), the \(f(x)\) values of an exponential function increase by a consistent multiplicative factor, which is a defining characteristic of exponential growth.