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 ?
To describe the lengths of the quilt using an experimental function, you would need to collect data on the number of folds required to fit the quilt inside the cubby for different lengths.
First, you would start by folding the quilt once and measuring the length after each fold. Repeat this process until the length is reduced to 1 meter. Record the number of folds required for each length.
Next, you would plot the data points with the length of the quilt on the x-axis and the corresponding number of folds on the y-axis. You can use a graphing tool or software to plot the points.
Once the points are plotted, you can try fitting different functions to the data to see which one best represents the relationship between the length and the number of folds. This can be done by plotting a curve or line that best fits the data points visually or by using regression analysis to find the equation of the curve that best fits the data. This equation would represent the experimental function describing the relationship between the lengths and the number of folds required.
Regarding the equation y = 2^x, this equation represents exponential growth or decay, where x is the input value and y is the output value. In this case, x represents the number of folds, and y represents the length of the quilt.
To determine the number of folds required for a length of 128 meters using this equation, you would plug in the value of 128 for y in the equation and solve for x.
Using the equation:
128 = 2^x
You would solve for x by taking the logarithm of both sides with base 2:
log₂(128) = log₂(2^x)
Simplifying further:
log₂(128) = x
Evaluating log₂(128), we get:
x ≈ 7
Therefore, it would take approximately 7 folds for the length of the quilt to reach 128 meters.