Question

Use the table to answer the question.

This table displays the
exponential growth of a
function over equal intervals

f(x) = a . bz

Co + Ax

α- b(z0+Δz)

xo +2Δx a- b(z0+2Δz)

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.

Ramona needs to subtract the z-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

Correct choice: "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."

Reason: for f(x)=a·b^{z},
f(x0+Δx)/f(x0)=a·b^{z0+Δz}/(a·b^{z0})=b^{Δz},
and likewise f(x0+2Δx)/f(x0+Δx)=b^{Δz}. The ratios are equal, so the function multiplies by the same factor over each equal interval.