Use the table to answer the question.

Question

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

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 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 the consecutive y
-values to calculate the growth factors.

Answer 1

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

In exponential functions of the form \( f(x) = a \cdot b^x \), the growth factor refers to the factor by which the function's output (y-value) increases as \( x \) increases by a specific amount (Δx). To find this growth factor, you compare the output for each successive input by dividing the y-value of the current input by the y-value of the previous input. Therefore, the correct response is that Avery should divide each y-value by the previous y-value to calculate the growth factors.