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 $10 million after 4 years, while profits increased $7.5 million per year. Select the correct graph of this function. gif There is a graph of a line that has a y intercept that is approximately negative $2 million and an x intercept that is approximately 0.7 years. There is a graph of a line that has a y intercept that is approximately negative $30 million and an x intercept that is approximately 3 years. There is a graph of a line that has a y intercept that is approximately negative $20 million and an x intercept that is approximately 2.7 years. There is a graph of a line passes through the point of x equals 0 comma y equals 0 and the point of x equals 4 comma y equals $10 million.

Answer 1

Given that a computer manufacturer built a new facility for assembling computers where they paid for construction and new equipment costs. This means that at the start of business by the company, the company has a negative profit.

Given that the company made combined profits of $10 million after 4 years, this means that the graph of the comany's profit against number of years will pass though point (4, 10 million)

Given that profits increased $7.5 million per year, this means that the slope of the graph of the comany's profit against number of years is $7.5 million.

The equation of a line passing though point
`(x_1,y_1)` with slope, m is given by

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

Thus given that the line passes through point (4, 10 million) and has a slope of 7.5 million, the equation of the line is given by

`y-10,000,000=7,500,000(x-4)=7,500,000x-30,000,000 \\ \\ y=7,500,000x-20,000,000`

At the y-intercept, i.e. when x = 0: y = 7,500,000(0) - 20,000,000 = 0 - 20,000,000 = -20,000,000

Thus the y-intercept is negative 20 million.

At the x-intercept, i.e. when y = 0: 0 = 7,500,000x - 20,000,000
7,500,000x = 20,000,000
x = 20,000,000 / 7,500,000 ≈ 2.7

Thus the x-intercept is approximately 2.7

Therefore, the correct graph of this function is a graph of a line that has a y-intercept that is approximately negative $20 million and an x-intercept that is approximately 2.7 years.