The formula for the growth rate of a population in the presence of a quantity x of food was given as the function below.  f ( x ) = Kx / ( A + x ) a. Find the rate of change of the growth rate with respect to the amount of food. b. The quantity A for the formula for f ( x ) represents the quantity of food for which the growth rate is half of its maximum. Using the answer from part a, find the rate of change of the growth rate when x = A.

Question

The formula for the growth rate of a population in the presence of a quantity x of food was given as the function below. 

f ( x ) = Kx / ( A + x )

a. Find the rate of change of the growth rate with respect to the amount of food.

b. The quantity A for the formula for f ( x ) represents the quantity of food for which the growth rate is half of its maximum. Using the answer from part a, find the rate of change of the growth rate when x = A.

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