On a golden eagle preserve the size of the golden eagle population depends upon the size of the population of rodents, the golden eagle’s primary source of food. Suppose that the number of eagles N is given by N=0.004x + 0.008x^2 where x is the number of rodents on the preserve. If the number of rodents available is increasing at the rate of 200 per year, how fast is the golden eagle population increasing when there are 500 rodents on the preserve?
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