Question

(a) make a scatter plot of the data in the table given to the right.
(b) find a power function that models the data.
(c) find a quadratic function that models the data.
(d) find a logarithmic function that models the data.
(a) choose the correct graph below.
(b) the equation of a power function that models the data is ( y=square )
(use integers or decimals for any numbers in the expression. round to three decimal places as needed.)

Explanation:

Step1: Input data into calculator

Enter the \(x\) - values (\(1,2,3,4,5,6\)) and \(y\) - values (\(3.5,5.2,6.4,7.2,7,8\)) into a graphing calculator or statistical software.

Step2: Select power regression

Use the power regression function (\(y = ax^{b}\)) on the calculator.
The general formula for power regression is \(y=ax^{b}\), where \(a\) and \(b\) are coefficients to be determined.
After performing the power regression on the data \((x_1 = 1,y_1=3.5),(x_2 = 2,y_2 = 5.2),(x_3=3,y_3 = 6.4),(x_4 = 4,y_4=7.2),(x_5 = 5,y_5 = 7),(x_6=6,y_6 = 8)\)
We get \(a\approx3.467\) and \(b\approx0.397\)

Answer:

\(y = 3.467x^{0.397}\)