Question

the table shows the total personal income in a country (in billions of dollars) for selected years from 1960 and projected to 2024. complete parts (a) through (d) below.

a. these data can be modeled by a quadratic function. write the equation of this function, with ( x ) equal to the number of years after 1960.

( y=square x^{2}+square x+square )

(type integers or decimals rounded to three decimal places as needed.)

Explanation:

Step1: Input data into calculator

Using a graphing calculator or software (like TI - 84 Plus: STAT → EDIT to input \(x\) (years after 1960: \(x = 0\) for 1960, \(x = 10\) for 1970, \(x = 20\) for 1980, \(x = 30\) for 1990, \(x = 40\) for 2000, \(x = 48\) for 2008, \(x = 54\) for 2014, \(x = 58\) for 2018, \(x = 64\) for 2024) and \(y\) (income values)).

Step2: Perform quadratic regression

Then use the STAT → CALC → QuadReg function.

Answer:

\(y = 0.504x^{2}+ 100.305x + 411.7\)