Question

My question is: The following table of the years of experience of university teachers and their corresponding salary in thousands of dollars.

Years of experience /salary
0yrs 58,000
5 yrs 68,000
10 yrs 78,000

a. Give the linear function S(t) that gives the annual salary in thousands of dollars for t years of experience

b. predict the average salary for a teacher with 15 years experience ( i think it is 82,000) but don't know how to work the problem

c. Find the years of experience for a teacher that is paid 84,000. (I think 12.5 but don't know how to show the work)

Answer 1

So, you will need to find the linear equation using the points given to you. What points? Well, lets see ;)

0 yrs, 58,000....This looks like a point! (0, 58 000).
5 yrs, 68,000....Another point! (5, 68000)

First find the gradient: \[m = \frac{y _{2} - y_{1}}{x_{2}-x_{1}}\]
Then find the equation of the line using the formula\[y -y_{1} = m(x-x_{1})\]

If you need help solving the equations or using the formulas post back :)

Answer 2

Alright, so as I said we first need to find the gradient. We have our points to do that.

(0,58000) and (5,68000).
(x1, y1) (x2,y2)

Substitute these into the formula
\[m = \frac{68000 - 58000}{5-0}\]\[m = 2,000\]

Now we must use the linear equation formula:
\[y - 58,000 = 2,000(x-0)\]\[y = 2,000x + 58,000\]

Change 'y' to S(t) and 'x' to t.\[S(t) = 2,000(t) + 58,000\]


For question b:
Substitute the time, 15 years, into the formula (so t = 15). \[S(15) = 2,000(15) + 58,000\]\[S(15) = 88,000\]

For question c:
Change S(t) to 84,000 and solve.
\[84,000 = 2,000t + 58000\]\[84,000 - 58,000 = 2,000t\]\[26,000 = 2,000t\]\[26,000 \div 2,000 = t\]\[t = 13\]
So, the answer is 13 years for c.

Answer 3

Thank you.