The total assets of a company in millions of dollars can be modeled by the function f(x)=-0.5^2 +5x+2 where x represents the number of years that have passed since the company was founded.
When the company was founded...
The highest value of total assets that the company had over its entire history was
when the function f(x) is at its maximum.
To find the maximum value of the function, we need to find the vertex of the parabola given by the function f(x). The x-coordinate of the vertex can be found using the formula x = -b/2a, where a = -0.5 and b = 5.
x = -5/(2*(-0.5)) = -5/-1 = 5
So, the vertex of the parabola is at x = 5.
To find the maximum value of the function, 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 highest value of total assets that the company had over its entire history was $14.5 million.