The total assets of a company in millions of dollars can be modeled by the function f(x)=−0.5x+5x+2 , where x represents the number of years that have passed since the company was founded.

When the company was founded, it had

A. 0

B. 2 million

C. 6.5 million

dollars.

3 answers

To find the total assets when the company was founded, we need to substitute x=0 into the function f(x) .

f(0) = -0.5(0) + 5(0) + 2
f(0) = 2

Therefore, the correct answer is:

B. 2 million dollars.
The highest value of total assets that the company had over its entire history was

A.10

B. 10.4

C. 14.5

million dollars.
To find the highest value of total assets, we need to find the vertex of the parabolic function represented by f(x) . The vertex of a parabola with equation f(x) = ax^2 + bx + c is given by the formula x = -b/(2a) .

In this case, the function representing the total assets is f(x) = -0.5x^2 + 5x + 2 . Therefore, a = -0.5 and b = 5 .

The x-coordinate of the vertex is given by:

x = -5 / (2*(-0.5))
x = -5 / -1
x = 5

To find the highest value of total assets, we substitute x = 5 into the function f(x) .

f(5) = -0.5(5)^2 + 5(5) + 2
f(5) = -0.5(25) + 25 + 2
f(5) = -12.5 + 25 + 2
f(5) = 14.5

Therefore, the correct answer is:

C. 14.5 million dollars.