SOLUTION: The logistic growth function f(t) = ((( 400 / 1+9.0e-0.22t ))) describes the population of a species of butterflies tmonths after they are introduced to a non-threatening habitat.

Algebra ->  Functions -> SOLUTION: The logistic growth function f(t) = ((( 400 / 1+9.0e-0.22t ))) describes the population of a species of butterflies tmonths after they are introduced to a non-threatening habitat.       Log On


   

Question 1060946: The logistic growth function f(t) = ((( 400 / 1+9.0e-0.22t ))) describes the population of a species of butterflies tmonths after they are introduced to a non-threatening habitat. How many butterflies are expected in the habitat after 12 months?
a. 480 butterflies
b. 401 butterflies
c. 244 butterflies
d. 4800 butterflies
Answer by KMST(5398) About Me  (Show Source):
You can put this solution on YOUR website!
What you meant is that t months after 40 butterflies are introduced, the habitat will contain f%28t%29=400%2F%281%2B9%2Ae%5E%28-0.22t%29%29 butterflies.
That tells you that for t=0 , f%280%29=40 ,
and f%28t%29 increases with t , but f%28t%29%3C400 at all times.
For t=12 , the approximate calculation (rounding to whole numbers) is
.

NOTE: Since the problem is multiple choice, with only one choice below 400,
and the function tells you that f%28t%29%3C400 at all times,
the only choice was c) 244 butteries.
No calculation was needed in this case.