Linear & Exponential Sequences

Question

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LESSON 9
Linear vs. Exponential Growth Rates

f (x) = a • br

a・60

xo + Ax a • 6(x0+Ax)

xо + 2Ax a • 3(20+2Ax)
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)
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.
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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 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 change in f(x)-values. She will be able to prove that exponential functions grow by equal differences over equal intervals.

Answer 1

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 is because, in exponential functions, the growth rate is multiplicative, meaning that each step over equal intervals results in the function value being multiplied by the same factor. This is distinct from linear functions, which grow by equal differences over equal intervals.