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

Answer:

The correct option is B.

Step-by-step 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

Answer:

The second graph is correct for this function.

Step-by-step 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.