Question

Please answer all parts to the question. when will the element be reduced to a minimum (in months) and what is the minimum percent? I will give thumbs up if you complete the whole question

A marshy region used for agricultural drainage has become contaminated with a particular element. It has been determined that flushing the area with clean water will reduce the element for a while, but it will then begin to build up again. A biologist has found that the percent of the element in the soil x months after the flushing begins is given by the function below. When will the element be reduced to a minimum? What is the minimum percent? x2 + 100 a , 15xs12 f(x) = 4x Find f'(x). x- 100 f'(x) = 442

Answer 1

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Hello Student! 429 f(x) = nutloo x² 100 Icas 12 an f (x) = at +10025 44 an f'(x) = I 2 = 9²-100. od 4 for 22 f'(x)=0 minima, 4x2] f(a) >0 and f(x)=0 h t flin) = 0 - 4 2.21) Al- 22 et 4 212 x² = 100 x= tlo (But lex {12 : Therefore n=10) At >=10, F"(x) = f'(W) - So - so so minima occurs at nalo +(10) = (10)²+ soo = lootloo - 200 = 5 4(10) 40 40 Element will be redund to win in n = 10 months and the min. percent will be f(10) 5 percent (Aus.) 1000