Question 13411
WOW!!  What an intimidating problem!

Let's try to simplify things a little bit.  First of all, you are given an incredibly intimidating formula:  {{{y= -5.05x^3 +3857x - 38411.25}}}, where y is 2400 and x is the unknown that you need to find:  the air-fuel ratio.


Substitute the value of y:
{{{2400 = -5.05x^3 + 3857x - 38411.25 }}}


Subtract 2400 from each side:
{{{0 = -5.05x^3 + 3857x - 38411.25 -2400 }}}
{{{ 0 = -5.05x^3 + 3857x - 40811.25 }}}


Now you have a really ugly equation to solve, and it looks like a real-life problem, probably one that is not going to come out even--it probably won't factor!  So use a graphing calculator to solve it.  


The problem is to graph {{{y = -5.05x^3 + 3857x - 40811.25 }}}, and find the x intercept(s).  That will be the solution.  Also, in the problem, it says that we are looking for values of x that are between 13 and 18.  The graph should look like this between x = 10 and x= 20 and y between -1000 and 1000:
{{{graph ( 300, 300, 10, 20, -1000, 1000, -5.05x^3 + 3857x - 40811.25 )}}}


There appear to be two points where the graph crosses the x axis within this interval.  With further calculation it seems that the first point is exact at x= 15.  The second number looks like 17, but it turns out to be approximately 16.89.  


Neat problem!!  Where did you get it?? 


R^2 at SCC