SOLUTION: Hello! In Indiana, the yield response, "y", of corn to nitrogen fertilizer, "n", can be modeled by: y(n)= -5.119+0.099n-0.004n^(3/2) 0< (or = to) n < (or = to) 500 whe

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: Hello! In Indiana, the yield response, "y", of corn to nitrogen fertilizer, "n", can be modeled by: y(n)= -5.119+0.099n-0.004n^(3/2) 0< (or = to) n < (or = to) 500 whe      Log On

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Question 1113478: Hello!
In Indiana, the yield response, "y", of corn to nitrogen fertilizer, "n", can be modeled by:
y(n)= -5.119+0.099n-0.004n^(3/2) 0< (or = to) n < (or = to) 500
where "n" is measured in kilograms per hectare, and "y" is measured in tons of corn per hectare.
1) Find the amount of nitrogen fertilizer which increases or decreases the yield.
2) How much fertilizer yields the maximum amount of corn per hectare?
3) What is the maximum yield?
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


You need some tool like a graphing calculator to analyze a function like that.

Here is a graph:

graph%28400%2C400%2C-50%2C625%2C-1%2C5%2C-5.119%2B0.099x-0.004x%5E%283%2F2%29%29

My graphing calculator (TI83) shows the maximum value to be y=3.86525 when n=272.25. So the answers to the questions are
(1) yield increases up to 272.25 kg/hectare of fertilizer and decreases for larger amounts of fertilizer
(2) maximum yield is with 272.25 kg/hectare of fertilizer
(3) the maximum yield is 3.86525 tons of corn per hectare