Question

The table shows a person’s annual salary y (in thousands of dollars) after x years of education beyond high school. What is the annual salary of the person after 8 years of education beyond high school? c. Find the annual salary of a person with 30 years of education. Do you think this situation makes sense? Explain.

Answer 1

Answer:

A.  The annual salary of the person after 8 years of education beyond high school will be $76,000.

C. The annual salary of the person after 30 years of education beyond high school will be $208,000.

The given situation does not make sense in real world.

Step-by-step explanation:

We have been given a table of values, which shows a person’s annual salary y (in thousands of dollars) after x years of education beyond high school.

A. First of all we will find the equation of the line form our given values.

We can see that our function is increasing at a constant rate as each next term is 12 more than the last term:

$40-28=12$

$52-40=12$

Let us find the slope of our given line using points (0,28) and (10,88) in slope formula.

$\text{Slope}=\frac{y_2-y_1}{x_2-x_1}$, where,

$y_2-y_1$ = Change in two y-coordinates.

$x_2-x_1$ = Change in same x-coordinates of two y-coordinates.

Upon substituting coordinates of our given points in slope formula we will get,

$\text{Slope}=\frac{88-28}{10-0}$

$\text{Slope}=\frac{60}{10}$

$\text{Slope}=6$

Since we know that slope-intercept form of an equation is: $y=mx+b$, where,

m = Slope of the line,

b = y-intercept or initial value.

We can see from our table that at x equals zero, y equals 28, so our y-intercept will be 28.

Upon substituting m=6 and b=28 in slope-intercept form of equation we will get,

$y=6x+28$

Therefore, the equation $y=6x+28$ represents the annual salary in thousands of dollars after x years of education beyond high school.

To find the salary of a person after 8 years of education beyond high school, let us substitute x=8 in our equation.

$y=6*8+28$

$y=48+28$

$y=76$

As the equation gives annual salary of a person in thousand dollars, therefore, the annual salary of the person after 8 years of education beyond high school will be $76,000.

C. To find the salary of a person with 30 years of education, we will substitute x=30 in our equation.

$y=6*30+28$

$y=180+28$

$y=208$

Therefore, the annual salary of the person after 30 years of education beyond high school will be $208,000.

Since a person does not study 30 years beyond high school, therefore, this situation does not make sense in real word.