Question

Tom just received a new job offer. He is told that his starting salary will be $75,000 per year. He is told his salary will probably be $81,000 in four years. We'll use this information to try to anticipate his future earnings in any given year.Assume that Y= Tom's salary amount in dollars and x= the number of years worked. Step 1.Use the data given to find the rate of change, or the salary increase per year.( hint: compute the slope.) We are now going to use a line to model Tom's salsry growth. Step 2. Use the data given and the slope value from Step 1 to write the slope-intercept form of the line. Step 3. Based on your equation from Step 2, What will Tom's salary be in ten years?

Answer 1

The answer is 90,000

Explanation:

So, what I did was take X(81,000) and subtracted it by Y(75,000) which came down to 6000, I then divided that number by 4 which gave me 1,500, (meaning his salary increases by 1,500 per year). Lastly I multiplied that number(1,500) by 10, and added it by 75,000 which gave me the answer of 90,000.

Answer 2

The salary increase per year is $1500. The slope intercept form is
`y=1500x+75000` and the salary in 10 years will be $90000.

Explanation:

Consider the provided statement.

His starting salary will be $75,000 per year.

Let x represents the number of years worked and Y is Tom's salary amount in dollars.

When he has 0 yr of experience the salary is $75000 per year.

Which can be written as (0,75000).

He is told his salary will probably be $81,000 in four years.

Therefore, when he has 4 yr of experience the salary is $81000 per year.

Which can be written as (4,81000).

STEP 1:

Now, find the rate of change by using the formula
`slope=m=(rise)/(run)`.

Calculate the rise by subtracting 75000 from 81000.

Rise = 81000 - 75000 = 6000

Now calculate the run by subtracting 0 from 4.

Run = 4 - 0 = 4

Substitute the respective values in the above formula.

`slope=m=(6000)/(4)`

`slope=m=1500`

Thus, the rate of change, or the salary increase per year is $1500.

STEP 2:

Now write the slope intercept form by using the formula:

`(y-y_1)=m(x-x_1)`

Substitute m = 1500 and
`(x_1,y_1)=(0,75000)` on the above formula.

`(y-75000)=1500(x-0)`

`y-75000=1500x`

`y=1500x+75000`

Hence, the slope intercept form is
`y=1500x+75000`.

STEP 3:

Now calculate the salary in 10 years.

Substitute the value of x = 10 in
`y=1500x+75000`.

`y=1500(10)+75000`

`y=15000+75000`

`y=90000`

Therefore, the salary in 10 years will be $90000.