Question

An industrial copy machine has the ability to reduce image dimensions by a certain percentage each time it copies. The original design started with a length of 16 inches, represented by the point (0,16). After going through the copy machine once, the length is 12, represented by the point (1,12). Enter the correct answer in the box by replacing the values of a and b in the equation f(x) = a(b)ˣ.

A) a = 16, b = 3/4
B) a = 16, b = 4/3
C) a = 12, b = 3/4
D) a = 12, b = 4/3

Answer 1

The original length of 16 inches decreases to 12 inches after going through the copy machine once. The correct equation to represent this relationship is f(x) = a(b)ˣ, with a = 16 and b = 3/4.

Step-by-step explanation:

Given that the original length is 16 inches and after going through the copy machine once, the length is 12 inches, we can determine the scaling factor by dividing the new length by the original length: 12/16 = 3/4.

The equation for the length of the copy after x number of times is f(x) = a(b)ˣ. In this case, the original length (a) is 16 and the scaling factor (b) is 3/4. Therefore, the correct answer is option A) a = 16, b = 3/4.