Question 468861: My teacher gave me this problem to solve and I don't understand how to work it out. Need help
Margarita is hired by an accounting firm at a starting salary of $58,000 per year. Three years later her annual salary has increased to $66,400. Assume her salary increases linearly.
a) Write the equation of a linear function that relates her annual salary, S, and the number of years, t, she has worked for the firm.
b) What does the slope of her salary function represent?
c) What does the S-intercept of her salary function represent?
d) Assuming the same rate of growth, after how many years with the firm will her salary first exceed $100,000? Describe what you did to arrive at your result.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! Margarita is hired by an accounting firm at a starting salary of $58,000 per year. Three years later her annual salary has increased to $66,400. Assume her salary increases linearly.
a) Write the equation of a linear function that relates her annual salary, S, and the number of years, t, she has worked for the firm.
b) What does the slope of her salary function represent?
c) What does the S-intercept of her salary function represent?
d) Assuming the same rate of growth, after how many years with the firm will her salary first exceed $100,000? Describe what you did to arrive at your result.
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Starting Salary is $58,000
She makes $66,400 in 3 years.
Salary is increasing linearly (in a straight line).
S = Salary
T = number of years.
her rate of growth is equal to (66,400 - 58,000) / 3 = $2,800 per year.
Since the annual growth is in the form of a straight line equation, it will take the form of S = m*T + b
m is the slope and b is the S intercept.
The slope is the change in Salary per year which is equal to $2,800.
the equation becomes:
S = 2800*T + b
The S intercept is the value of S when T = 0.
When T = 0, she was just starting and her salary was $58,000, so the value of b is equal to $58,000.
the equation becomes:
S = 2800*T + 58000
The * is the multiplication symbol.
2800*T is equivalent to 2800 times T.
The equation is S = 2800*T + 58000 as stated above.
The questions can now be answered.
They are:
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a) Write the equation of a linear function that relates her annual salary, S, and the number of years, T, she has worked for the firm.
S = 2800 * T + 58000
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b) What does the slope of her salary function represent?
It represents the change in salary each year.
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c) What does the S-intercept of her salary function represent?
It represents her starting salary.
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d) Assuming the same rate of growth, after how many years with the firm will her salary first exceed $100,000? Describe what you did to arrive at your result.
The equation is S = 2800 * T + 58000
S will be equal to $100,000, so replace S with that figure in the equation to get:
100000 = 2800 * T + 58000
subtract 58000 from both sides of this equation to get:
42000 = 2800 * T
divide both sides of this equation by 2800 to get:
T = 15.
She will reach a salary of $100,000 per year in the 15th year of her employment.
We can graph this equation, but we have to replace S with y and T with x in order to do that.
the equation becomes:
y = 2800 * x + 58000
We'[ll graph that equation for 20 years out into the future.
The graph of that equation is shown below:
I drew 3 horizontal lines at y = 58000 and y = 66400 and y = 100000 so you can spot the year in which those values occur easier.
just grace a vertical line down from the intersection of those horizontal lines with the line of the equation to get an approximate estimate of the year in which they occur.
the year should be 0, 3, and 15 which can be confirmed easily by replacing x in the equation with 0, 3, and 15, and solving for y.
Note the equation is the same:
S = 2800 * T + 58000 is exactly the same equation as:
y = 2800 * x + 58000.
Only the names have been changed to protect the innocent.
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