Question

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?

Answer 1

the linear equation is :

y= -2625x+5737875

and 440000 employees will be in year 2271

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:

`y-y1 = (y2-y1) (x-x1)/(x2-x1)`

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

`y - 522000 = (480000-522000)/(2003-1987)  (x-1987)\\y- 522000 = -2625(x-1987)\\y- 522000= -2625x+5215875\\\\y= -2625x+5737875`

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

`440000= -2625x+ 5737875\\\\2526x = 5737875 -440000\\2526x =  5736555\\x= (5736555)/(2526) \\x= 2271`