SOLUTION: In 1986, 523,000 people worked in the air transportation industry. In 2002, the number was 485,000. (a) Find a linear equation giving the number of employees in the air transpor

Algebra ->  Finance -> SOLUTION: In 1986, 523,000 people worked in the air transportation industry. In 2002, the number was 485,000. (a) Find a linear equation giving the number of employees in the air transpor      Log On


   

Question 1153736: In 1986, 523,000 people worked in the air transportation industry. In 2002, the number was 485,000.
(a) Find a linear equation giving the number of employees in the air transportation industry in terms of​ x, the number of years since 1986.
(b) Assuming the equation remains valid in the​ future, in what year will there be 430,000 employees of the air transportation​ industry?
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
In 1986, 523000 people worked in the air transportation industry.
In 2002, the number was 485000.

(a) Find a linear equation giving the number of employees in the air transportation industry in terms of​ x, the number of years since 1986.
x=6 in 1986
let the number of employees be y divided by 1000 to make it simplier

linear equation is: y=mx%2Bb

given two points:
(6,523)
(16,485)


use points to find a slope m
m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29
m=%28485-523%29%2F%2816-6%29
m=%28-38%29%2F10
m=-3.8


y=-3.8x%2Bb

use one point to find b

523=-3.8%2A6%2Bb
523=-22.8%2Bb
b=523%2B22.8
b=545.80


so, equation is
y=-3.8x%2B545.8


(b) Assuming the equation remains valid in the​ future, in what year will there be 430000 employees of the air transportation​ industry?

y=430
430=-3.8x%2B545.8
3.8x=545.8-430
3.8x=115.8
x=115.8%2F3.8
x=30.4737

we started with year 1986, so add 30.4737years
a year will be in 1986%2B30.4737=2016.4737
middle of 2016


check:
so, now x=30.4737
430=-3.8%2A30.4737%2B545.8
430=-115.8%2B545.8
430=483


Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
In 1986, 523,000 people worked in the air transportation industry. In 2002, the number was 485,000.
(a) Find a linear equation giving the number of employees in the air transportation industry in terms of​ x, the number of years since 1986.
(b) Assuming the equation remains valid in the​ future, in what year will there be 430,000 employees of the air transportation​ industry?
You need to IGNORE almost ALL responses by this person, as a great many of them are WRONG!

Even my 4th grader knows that from 1986 to 2002 spans a total of 16 years, NOT 10!

The points you're looking for are: (0, 523) and (16, 485), with the number in 000s of individuals, and the equation is: 

For b), replace f(x) or y with 430 (in thousands), and you'll get a decimal that you should ROUND UP to get the number of years, after 1986 that the number

of employees will reach 430,000. Add that number to 1956 to get the actual YEAR!!