Question

the table shows the wavelength of the sound produced by keys on a piano x keys away from the a above middle c. sound wavelength number of keys above the a above middle c wavelength (cm) 0 78.41 2 69.85 3 65.93 6 55.44 10 44.01 using the exponential regression model, which is the best prediction of the wavelength of the key that is 8 above the a above middle c? 49.31 cm 49.44 cm 49.73 cm 49.78 cm

Explanation:

Step1: Input data into calculator

Input the data \((x,y)\) where \(x\) is the number of keys above the \(A\) above middle \(C\) and \(y\) is the wavelength (\(cm\)) into a graphing calculator for exponential regression.

Step2: Find the exponential regression equation

The general form of an exponential regression equation is \(y = ab^{x}\). After running the exponential regression on the data \((0,78.41),(2,69.85),(3,65.93),(6,55.44),(10,44.01)\), we get \(y\approx78.41\times(0.94)^{x}\)

Step3: Substitute \(x = 8\) into the equation

When \(x = 8\), we calculate \(y=78.41\times(0.94)^{8}\)

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Answer:

\(49.31\ cm\)