Question

Use the table to answer the question.

Make the table like the one to calculate the growth factor for the given values of x and f(x).
x
f(x)=a⋅bx
Growth Factor
x0
a⋅bx0

x0+Δx
a⋅b(x0+Δx)

x0+2Δx
a⋅b(x0+2Δx)

Avery wants to use the table to prove something about how exponential functions grow. She’s not sure what to put in the “growth factor” column. How should she calculate the two missing growth factors?

(1 point)
Responses

Avery should subtract the consecutive y
-values to calculate the growth factors.
Avery should subtract the consecutive y -values to calculate the growth factors.

Avery should divide each y
-value by the previous y
-value to calculate the growth factors.
Avery should divide each y -value by the previous y -value to calculate the growth factors.

Avery should subtract each x
-value from the corresponding y
-value.
Avery should subtract each x -value from the corresponding y -value.

Avery should divide each y
-value by its corresponding x
-value.

Answer 1

Correct choice: Avery should divide each y-value by the previous y-value to calculate the growth factors.

Calculation:
- Growth factor from x0 to x0+Δx = (a·b^(x0+Δx)) / (a·b^x0) = b^(Δx).
- Growth factor from x0+Δx to x0+2Δx = (a·b^(x0+2Δx)) / (a·b^(x0+Δx)) = b^(Δx).

So both missing growth factors are b^(Δx).