Write Linear Functions to describe this situation

Question

Suppose the annual salary of a lecturer at a university is a linear function of the number of years of teaching experience. A lecturer with 9 years of experience is paid $41, 350. A lecturer with 15 years experience of teaching experience is paid $46, 687.

 

A). Write a linear function to describe this situation.

B). Use the function to determine the salary of a lecturer with 10 years of experience.

C). Estimate how many years of teaching experience a lecturer must have to earn a salary of $44, 908. 

Answer 1

A. The slope of the line is (46687 - 41350)/(15 - 9) = 889.5.Using the         point-slope form for the equation of a line, we get

        y - 41350 = 889.5(x - 9)

        y - 41350 = 889.5x - 8005.5

   So, y = 889.5x +33344.5

 

B. If x = 10, then y = 889.5(10) + 33344.5 = $42239.5

 

C.  If y = 44908, then 44908 = 889.5x + 33344.5

                                889.5x = 11563.5

                                        x = 13 years

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Answer 2

Use 9 years as base year

Find increment per year from 9 to 15 years => (46687 - 41350)/6 = 889.5

 

(A)salary = 41350 + 889.5n

where is n is numer of years of experience in addition to 9 years

(B) salary in 10 years = 41350 + 889.5x1 = 40,460.5

 

(C) 44908 = 41350 + 889.5

 

n = 4 years

total teaching experienc = 9 + 4 = 13 years

:)