Expert: Richard J. Raridon - 9/24/2008

Question
Help!  I am trying to help my 10th grader with her homework and we can't figure this out.

An exclusive restaurant is open from 3:00 to 10:00 p.m.  Each evening, the number of people served S increases steadily and then decreases according to the model
S=-30|t-6.5|+105 where t=0 represents 12:00 p.m.

1.  Graph the function
2.  find the vertex of the graph.   Explain what each coordinate of the vertex represents.  

Answer
S(t) = -30|t-6.5|+105
t = 3 to 10
I can't graph it for you but you can do it.  Simply put in a value for t, calculate S(t) and plot S(t) vs. t.  
For example, S(3) = 0 and S(10) = 0 and it's obvious that the maximum value occurs when t = 6.5 so that's the vertex and S(6.5) gives you the maximum number of people served.