To determine the function [tex]\(F(x)\)[/tex] that describes the funds raised as a function of the number of tickets sold, we need to calculate the difference between the revenue function [tex]\(R(x)\)[/tex] and the cost function [tex]\(C(x)\)[/tex].
Given:
[tex]\[ R(x) = 0.05x^3 - 75 \][/tex]
[tex]\[ C(x) = 30x + 12,500 \][/tex]
The funds raised, [tex]\(F(x)\)[/tex], can be represented as:
[tex]\[ F(x) = R(x) - C(x) \][/tex]
Substituting the given functions [tex]\(R(x)\)[/tex] and [tex]\(C(x)\)[/tex] into the equation:
[tex]\[ F(x) = (0.05x^3 - 75) - (30x + 12,500) \][/tex]
Now, we will distribute the negative sign and combine like terms:
[tex]\[ F(x) = 0.05x^3 - 75 - 30x - 12,500 \][/tex]
[tex]\[ F(x) = 0.05x^3 - 30x - 75 - 12,500 \][/tex]
[tex]\[ F(x) = 0.05x^3 - 30x - 12,575 \][/tex]
Therefore, the function describing the funds raised, [tex]\(F(x)\)[/tex], is:
[tex]\[ F(x) = 0.05x^3 - 30x - 12,575 \][/tex]
So the correct answer is:
[tex]\[ \boxed{F(x)=0.05 x^3-30 x-12,575} \][/tex]
