the table shows the wavelength of the sound produced by keys on a piano x keys away from the a above middle…

the table shows the wavelength of the sound produced by keys on a piano x keys away from the a above middle c. 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?\nsound wavelength\nnumber of keys above the a above middle c | wavelength (cm)\n0 | 78.41\n2 | 69.85\n3 | 65.93\n6 | 55.44\n10 | 44.01\n49.31 cm\n49.44 cm\n49.73 cm\n49.78 cm

the table shows the wavelength of the sound produced by keys on a piano x keys away from the a above middle c. 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?\nsound wavelength\nnumber of keys above the a above middle c | wavelength (cm)\n0 | 78.41\n2 | 69.85\n3 | 65.93\n6 | 55.44\n10 | 44.01\n49.31 cm\n49.44 cm\n49.73 cm\n49.78 cm

Answer

Answer:

A. 49.31 cm

Explanation:

Step1: Assume exponential regression model

Let the exponential regression model be $y = ab^{x}$, where $x$ is the number of keys above the A above middle - C and $y$ is the wavelength.

Step2: Use statistical software or calculator

Input the data points $(0,78.41),(2,69.85),(3,65.93),(6,55.44),(10,44.01)$ into a statistical software or a calculator with exponential regression function.

Step3: Get the regression equation

After running the regression, we get the equation (the actual coefficients depend on the software/calculator used).

Step4: Substitute $x = 8$

Substitute $x = 8$ into the obtained exponential regression equation $y = ab^{x}$ to find the predicted wavelength. After calculation, we find that the predicted value is closest to 49.31 cm.