(a) What is the carrying capacity of theenvironment? 1 eagles (b) What is the pr

Question

(a) What is the carrying capacity of theenvironment?
1 eagles
(b) What is the predicted population of this species of Americanbald eagle in 12 years?
2 eagles
(c) When will the population be 340?
3 years Often environmentalists will capture an endangered species andtransport the species to a controlled environment where the speciescan produce offspring and regenerate its population. Suppose thatsix American bald eagles are captured, transported to Montana, andset free. Based on experience, the environmentalists expect thepopulation to grow according to the model below where t ismeasured in years. (a) What is the carrying capacity of theenvironment? 1 eagles (b) What is the predicted population of this species of Americanbald eagle in 12 years? 2 eagles (c) When will the population be 340? 3 years

Explanation / Answer

PART A>>> The carrying capacity is the number of eaglesas t approaches . For this value of t, the exponentialterm in the denominator approaches zero, and thus the carryingcapacity is 500/1 or 500 eagles.

PART B>>>   plug in t = 12 and use calculatorto get   500 / 12.927   =   38.7eagles.

PART C>>>   plug in P = 340, and solve fort.

   340 ( 1 + 83.33 e - .162 t ) = 500

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