# Math Help - exponential function

1. ## exponential function

A quilt is 100 m. long and 1 meter wide
It has to folded to 1 meter for it to fit inside the cubby.
How can experimental function be used to describe the lengths???

Also, How could you use y=2^x to determine the # of folds for the length of 128 ?

2. For the length L as a function of the number of folds x,
$L(x) = 100 \left(\frac{1}{2}\right)^{x}$
looks like it will work. Fold it once, the quilt will be 50m long. Fold it a second time, the quit will be 25m long. To find out how many folds it will take to fit the quilt into the cubby, set the L(x) equal to 1.

If the initial length is 128m, then the function would be
\begin{aligned}
L(x) &= 128 \left(\frac{1}{2}\right)^{x} \\
&= 2^7 \cdot 2^{-x} \\
&= 2^{7 - x}
\end{aligned}

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