The following function gives the cost, in dollars, of producing x kilograms of fertilizer: C(x)=0.001x^(3)-0.14x^(2)+7x+160 What is the instantaneous rate of change of the cost when 50 kilograms are produced? Choose 1 answer: (A) -6.5 kilograms per dollar (B) -6.5 dollars per kilogram (C) 0.5 kilograms per dollar (D) 0.5 dollars per kilogram

Question

The following function gives the cost, in dollars, of producing  x kilograms of fertilizer:  C(x)=0.001x^(3)-0.14x^(2)+7x+160 What is the instantaneous rate of change of the cost when 50 kilograms are produced? Choose 1 answer: (A) -6.5 kilograms per dollar (B) -6.5 dollars per kilogram (C) 0.5 kilograms per dollar (D) 0.5 dollars per kilogram

Bytelearn · Accepted Answer

Calculate Derivative: To find the instantaneous rate of change, we need to calculate the derivative of the cost function C(x) with respect to x.Find C'(x): Differentiate C(x) = 0.001x^3 - 0.14x^2 + 7x + 160 with respect to x to get C'(x). C'(x) = 0.003x^2 - 0.28x + 7Evaluate at x=50: Evaluate C'(x) at x = 50 to find the instantaneous rate of change at that point. C'(50) = 0.003(50)^2 - 0.28(50) + 7Calculate C'(50): Calculate the value of C'(50). C'(50) = 0.003(2500) - 0.28(50) + 7 C'(50) = 7.5 - 14 + 7 C'(50) = 0.5Final Instantaneous Rate: The instantaneous rate of change of the cost when 50 kilograms are produced is 0.5 dollars per kilogram, which corresponds to answer choice (D).

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