An individual's income varies with age. The table shows the median income I of individuals of different age groups within the United States for a certain year. For each age group, let the class midpoint represent the independent variable x. For the class "65 years and older," assume that the class midpoint is 69.5. Complete parts (a) through (e). (a) Use a graphing utility to draw a scatter diagram of the data. Comment on the type of relation that may exist between the two variables. Which type of relation exists between the two variables? (b) Use a graphing utility to find the quadratic function of best fit that models the relation between age and median income.The quadratic function of best fit is y=___x2+_____x−____. (c) Use the function found in part (b) to determine the age at which an individual can expect to earn the most income. At about_____years of age, the individual can expect to earn the most income.(Do not round until the final answer. Then round to the nearest tenth as needed.) (d) Use the function in part (b) to predict the peak income earned.The predicted peak income is about $_____.(Round to the nearest dollar as needed.) (e) With a graphing utility, graph the quadratic function of best fit on the scatter diagram. [0,80,10] by [0,60000,10000] ClassAgeMidpoint, MedianIncome, I$12,96515-24 years25-34 years35-44 years45-54 years55-64 years65 years and older19.529.5$32,13139.5$43,63849.5$46,69359.5$40,47669.5$22,500

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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An individual's income varies with age. The table shows the median income I of individuals of different age groups within the United States for a certain year. For each age group, let the class midpoint represent the independent variable x. For the class "65 years and older," assume that the class midpoint is 69.5.

Complete parts (a) through (e).

(a) Use a graphing utility to draw a scatter diagram of the data. Comment on the type of relation that may exist between the two variables.

Which type of relation exists between the two variables?

(b) Use a graphing utility to find the quadratic function of best fit that models the relation between age and median income.

The quadratic function of best fit is y=___x2+_____x−____.

At about_____years of age, the individual can expect to earn the most income.

(Do not round until the final answer. Then round to the nearest tenth as needed.)

(d) Use the function in part (b) to predict the peak income earned.

The predicted peak income is about $_____.

(Round to the nearest dollar as needed.)

(e) With a graphing utility, graph the quadratic function of best fit on the scatter diagram.

[0,80,10] by [0,60000,10000]

Class
Age
Midpoint, Median
Income, I
$12,965
15-24 years
25-34 years
35-44 years
45-54 years
55-64 years
65 years and older
19.5
29.5
$32,131
39.5
$43,638
49.5
$46,693
59.5
$40,476
69.5
$22,500

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