SOLUTION: 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.

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: 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.       Log On


   



Question 933700: 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 by MathLover1(20850) About Me  (Show Source):
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a linear function:
y=mx%2Bb
A). Write a linear function to describe this situation.
A lecturer with 9 years of experience is paid $41350.
x=9 and y=41350
41350=m%2A9%2Bb ....eq.1
A lecturer with 15 years experience of teaching experience is paid $46687.
x=15 and y=46687
46687=m%2A15%2Bb ....eq.2
solve this system to find m and b
41350=9m%2Bb ....eq.1
46687=15m%2Bb ....eq.2
_________________.....subtract eq.1 from eq.2
46687-41350=15m%2Bb-%289m%2Bb%29
5337=15m%2Bcross%28b%29-9m-cross%28b%29
5337=6m
5337%2F6=m
m=889.5
go to eq.1 substitute m and solve for b
41350=9%2A889.5%2Bb ....eq.1
41350=8005.5%2Bb
41350-8005.5=b
b=33344.5
your equation is:
y=889.5x%2B33344.5

B). Use the function to determine the salary of a lecturer with 10 years of experience.
x=10
y=889.5%2A10%2B33344.5
y=8895%2B33344.5
y=42239.5
C). Estimate how many years of teaching experience a lecturer must have to earn a salary of $44908.
44908=889.5x%2B33344.5
44908-33344.5=889.5x
11563.5=889.5x
11563.5%2F889.5=x
13=x years of teaching experience a lecturer must have to earn a salary of $44908