Question

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

the power function is ( y = 3.1x^{0.6} ).
(type integers or decimals rounded to three decimal places as needed.)

Explanation:

Step1: Recall the power function form

The power function has the form \(y = ax^{b}\).

Step2: Use a calculator or software for power - regression

Using a graphing calculator or statistical software (such as Excel's regression tool with a power - regression option), input the \(x\) and \(y\) values from the table \((x = 1,2,\cdots,8;y = 3.1,4.6,\cdots,10.6)\).
After performing the power - regression analysis:
The coefficient \(a\approx3.1\) and the exponent \(b\approx0.6\)

Answer:

The power function is \(y = 3.1x^{0.6}\)