A company finds that its sales since the company started in 2000 can be modeled by the function
$s(t)=(20t^2+800t+300)/(8t^2+10t+100)$
where $s$ is the total sales, in millions of dollars, and t is the number of years since 2000.
Calculate the years when sales are 9 million, algebraically.
What I understand from the question is that I need to solve for $t$ when $s(t)=9$. However, I get two answers (positive and negative). How do I rewrite these answers to model the number of years? Also, how do I use this model to predict what sales would be like after many years?
Double check your solution - no negative! $$s(t)=\frac{20t^2+800t+300}{8t^2+10t+100}=9 \Rightarrow 52t^2-710t+600=0 \Rightarrow \\ t_{1,2}=\frac{355\pm \sqrt{3793}}{52}\approx 0.9; 12.7.$$ Can you figure out the years starting from $2000$?
Also, note that if in another problem you get a negative number for time, you can ignore it and accept only the positive, that is meaningful numbers!