SOLUTION: The population of a certain species of birds on an island is limited by the type of habitat required for nesting. The population grows according to the function N(t)=28000/5+13.5e

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: The population of a certain species of birds on an island is limited by the type of habitat required for nesting. The population grows according to the function N(t)=28000/5+13.5e      Log On


   

Question 1168672: The population of a certain species of birds on an island is limited by the type of habitat required for nesting. The population grows according to the function
N(t)=28000/5+13.5e^−0.038t, where t is measured in years. Find the initial bird population. What is the maximum population that the environment will support? (i.e. as t→∞ what does N(t) approach?).According to the model, what will the population be in 10 years? Numeric answer only. Make sure to round your answer correctly.
Found 2 solutions by Boreal, htmentor:
Answer by Boreal(15235) About Me  (Show Source):
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No is at t=0
this is 28000/(5+13.5)=1513.51 or 1514.
maximum population will be 28000/5=5600
in 10 years, it will be e^(-0.38), this makes N(10)=1967.38 or 1967
graph%28300%2C300%2C-50%2C250%2C-200%2C6000%2C28000%2F%285%2B13.5e%5E%28-0.038x%29%29%29
graph%28300%2C300%2C-5%2C20%2C-100%2C2500%2C28000%2F%285%2B13.5e%5E%28-0.038x%29%29%29

Answer by htmentor(1343) About Me  (Show Source):
You can put this solution on YOUR website!
I'm assuming you mean N(t) = 2800/(5+13.5e^−0.038t)
The initial population is N(0) = 2800/(5+13.5e^0) = 2800/(5+13.5) = 1513.51 -> 1514
As t→∞, the negative exponential goes to 0. Thus the maximum population is = 28000/5 = 5600
N(10) = 1967.38 -> 1967