In 1987, 522 comma 000 people worked in the air transportation industry. In 2003, the number was 480 comma 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 1987. (b) Assuming the equation remains valid in the future, in what year will there be 440 comma 000 employees of the air transportation industry?

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najamraza najamraza · Answer 1 · 2019-12-11T10:24:03+01:00

Answer:

the linear equation is :

y= -2625x+5737875

and 440000 employees will be in year 2271

Step-by-step explanation:

in order to find the linerar equation let us first convert the given data into (x,y ) co-ordinates i.e

x1= 1987 y1= 522,000

and

x2= 2003, y2 = 480000

according to two point form:

[tex]y-y1 = (y2-y1) \frac{x-x1}{x2-x1}[/tex]

In this example we have x1=1987 , y1=522000 , x2=2003 and y2=480000. So,

[tex]y - 522000 = \frac{480000-522000}{2003-1987} (x-1987)\\y- 522000 = -2625(x-1987)\\y- 522000= -2625x+5215875\\\\y= -2625x+5737875[/tex]

now to find the year when there will be 440000 employs working , we simply put y= 440000 in the above derived equation

[tex]440000= -2625x+ 5737875\\\\2526x = 5737875 -440000\\2526x = 5736555\\x= \frac{5736555}{2526} \\x= 2271[/tex]