Question

A computer manufacturer built a new facility for assembling computers. There were construction and new equipment costs. The company paid for these costs and made combined profits of $40 million after 4 years while profits increased $30 million per year. Select the correct graph of this function.

Answer 1

The correct option is B.

Explanation:

Consider the provided information.

The company paid for these costs and made combined profits of $40 million after 4 years while profits increased $30 million per year.

Let time represents by x axis and profit represented by y axis.

Therefore, the x and y coordinates from the provided information is: (4,40)

It is given that the profit increased $30 million per year, that means the slope of the line is 30.

The slope intercept form is:
`y=mx+c`

Substitute the respective values.

`40=30(4)+c`

`40=120+c`

`-80=c`

Hence, the y intercept is (0,-80).

Now consider the provided graph of the function.

Only, the Graph B has y intercept (0,-80)

Therefore, the correct option is B.

Answer 2

The second graph is correct for this function.

Explanation:

The company made combined profits of $40 million after 4 years. The profits increased $30 million per year.

Therefore the rate of change of profit function is 30 and the graph of profit function passing through the point (4,40).

Point slope of a linear function is

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

`y-40=30(x-4)`

`y-40=30x-120`

Add 40 both sides.

`y=30x-80`

Therefore the profit function is defined as

`y=30x-80`

Put x=0

`y=30(0)-80`

`y=-80`

Therefore y-intercept of function is -80. So, second graph is correct for this function.

Y-intercept of first graph is positive and y-intercept of third and fourth graph are more that -50, therefore option 1, 3 and 4 are incorrect.