Concept explainers
Population of anEndangered Species Often environmentalists capture an endangered species and transport the species to a controlled environment where the species can produce offspring and regenerate its population. Suppose that six American bald eagles are captured, transported to Montana, and set free. Based on experience, the environmentalists expect the population to grow according to the model
where t is measured in years.
Determine the carrying capacity of the environment.
What is the growth rate of the bald eagle?
What is the population after 3 years?
When will the population be 300 eagles?
How long does it take for the population to reach one-half the carrying capacity?
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Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
- Suppose that a particular plot of land can sustain 500 deer and that the population of this particular species of deer can be modeled according to the logistic model as dPdt=0.2(1P500)P. Each year, a proportion of the herd deer is sold to petting zoos. a. Find the function that gives the equilibrium population for various proportions. b. Determine the maximum number of deer that should be sold to petting zoos each year. Hint: Find the maximum sustainable harvestarrow_forwardWhat is the carrying capacity for a population modeled by the logistic equation P(t)=250,0001+499e0.45t ? initial population for the model?arrow_forward
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