Answer
a. $6$ years.
b. See point on the graph.
Work Step by Step
a. Given $P=-10x^2+475x+3500$. let $P=5990$, we have $-10x^2+475x+3500=5990$ or $2x^2-95x+498=0$ which can be factored as $(x-6)(2x-83)=0$. As $0\leq x\leq 12$, we have $x=6$ years.
b. The coordinates of the point are $(6,5990)$ and we can mark the point on the curve as shown in the figure.
