Question

find the power function that models the data in the table below.

the power function is ( y=square x^{square} ).
(type integers or decimals rounded to three decimal places as needed.)

Explanation:

Step1: Enter data into calculator

Enter the \(x\) - values (\(1,2,\cdots,8\)) and \(y\) - values (\(3.1,4.6,\cdots,10.6\)) into a graphing calculator or statistical software.

Step2: Use power - regression function

Use the power - regression feature (\(y = ax^{b}\)).
For a TI - 84 Plus calculator, go to STAT → EDIT to input the data. Then go to STAT → CALC → PwrReg.
The calculator will give the values of \(a\) and \(b\).
After performing the power - regression on the given data:
The value of \(a\approx2.500\) and \(b\approx0.500\)

Answer:

The power function is \(y = 2.5x^{0.5}\)