SOLUTION: sketch the graph of f(x)=12/1+3e-0.2x'. label the asymptotes and the y-intercept Also: a population of rabbits in a zoo can be modeled by the function P(t)=1500/1+38e-0.8t' wher

Algebra ->  Rational-functions -> SOLUTION: sketch the graph of f(x)=12/1+3e-0.2x'. label the asymptotes and the y-intercept Also: a population of rabbits in a zoo can be modeled by the function P(t)=1500/1+38e-0.8t' wher      Log On


   

Question 1127638: sketch the graph of f(x)=12/1+3e-0.2x'. label the asymptotes and the y-intercept
Also:
a population of rabbits in a zoo can be modeled by the function P(t)=1500/1+38e-0.8t' where P(t) is the number of individuals and t is the number of yeras. what is the carrying capacity of the zoo?
Answer by greenestamps(13209) About Me  (Show Source):
You can put this solution on YOUR website!


(a) Here is a graph, showing the horizontal asymptote; you can make your own sketch and do the labeling.

graph%28400%2C400%2C-2%2C40%2C-2%2C15%2C12%2C12%2F%281%2B3e%5E%28-0.2x%29%29%29

(b)
P%28t%29+=+1500%2F%281%2B38e%5E%28-0.8t%29%29

This is the standard form of a logistic function. When t gets very large, the exponential in the denominator goes to 0, so the whole denominator goes to 1; that means the numerator in the logistic function is the maximum value of the function, which is called carrying capacity.

So in this problem the carrying capacity for the rabbits in the zoo is 1500.