1)
The total assets of a company in millions of dollars can be modeled by the function f (x) = -0.5x^2+5x+2, where x represents the number of years that have passed since the company was founded.
When the company was founded, it had
(1 point)
0
2 million
6.5 million
dollars.
To find the initial assets when the company was founded, we need to find the value of f(0).
f(0) = -0.5(0)^2 + 5(0) + 2
f(0) = 2
So, when the company was founded, it had 2 million dollars.
Therefore, the correct answer is:
2 million dollars.
The highest value of total assets that the company had over its entire history was
(1 point)
Ο 10
Ο 10.4
Ο 14.5
million dollars.
To find the highest value of total assets the company had over its entire history, we need to find the vertex of the parabolic function f(x) = -0.5x^2 + 5x + 2.
The x-coordinate of the vertex of a parabola given by the function f(x) = ax^2 + bx + c is given by x = -b / 2a.
In this case, a = -0.5 and b = 5.
x = -5 / 2(-0.5) = -5 / -1 = 5
To find the corresponding y-coordinate, we substitute x = 5 into the function:
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 highest value of total assets that the company had over its entire history was 14.5 million dollars.
The correct answer is:
Ο 14.5 million dollars.