Government economists in a certain country have determined that the demand equation for soybeans is given by p = f (x) = 57 2x2 + 1 where the unit price p is expressed in dollars per bushel and x, the quantity demanded per year, is measured in billions of bushels. the economists are forecasting a harvest of 2.4 billion bushels for the year, with a possible error of 10% in their forecast. use differentials to approximate the corresponding error in the predicted price per bushel of soybeans. (round your answer to one decimal place.)

Question

Delilah Le

Business

21 May, 04:12

Government economists in a certain country have determined that the demand equation for soybeans is given by p = f (x) = 57 2x2 + 1 where the unit price p is expressed in dollars per bushel and x, the quantity demanded per year, is measured in billions of bushels. the economists are forecasting a harvest of 2.4 billion bushels for the year, with a possible error of 10% in their forecast. use differentials to approximate the corresponding error in the predicted price per bushel of soybeans. (round your answer to one decimal place.)

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Isis Kidd · Answer 1

=>

|∆p| = |dp/dx|∙|∆x|

= | d{ 56 / (2∙x² + 1) ]/dx | ∙ |∆x|

= | 56∙ (-1) ∙2∙ (2x) / (2∙x² + 1) ² ] | ∙ |∆x|

= | - 224∙x / (2∙x² + 1) ² | ∙ |∆x|

for

x = 1.9

∆x = 0.1∙1.9 = 0.19

|∆p| = 224∙1.9 / (2∙ (1.9) ² + 1) ² | ∙ |0.19| = 1.197

That is about twice of your result. Maybe you forget a factor 2 in the numerator while taking the derivative.