Question

origami is the traditional japanese art of paper folding. as an introduction to an origami art project, an art teacher asks students to try to fold a piece of paper in half as many times as they can. the exponential function $f(x) = 2^x$ can be used to determine the number of layers of paper created based on the number of folds, $x$. which statement describes the rate of change of the layers of paper? the number of layers increases by 4 for each additional fold. the number of layers increases by a factor of 4 for each additional fold. the number of layers increases by 2 for each additional fold. the number of layers increases by a factor of 2 for each additional fold.

Explanation:

Step1: Evaluate f(x) for x=0,1,2

$f(0)=2^0=1$, $f(1)=2^1=2$, $f(2)=2^2=4$

Step2: Compare consecutive values

$\frac{f(1)}{f(0)}=\frac{2}{1}=2$, $\frac{f(2)}{f(1)}=\frac{4}{2}=2$

Step3: Analyze rate of change

Each fold multiplies layers by 2, not adding a constant.

Answer:

The number of layers increases by a factor of 2 for each additional fold.