SOLUTION: Ten goats were set loose in an island and their population growth can be approximated by the function: p(t)=greatest integer function of [60(t+1)] / (t+6) where p represents th

Algebra ->  Rational-functions -> SOLUTION: Ten goats were set loose in an island and their population growth can be approximated by the function: p(t)=greatest integer function of [60(t+1)] / (t+6) where p represents th      Log On


   

Question 1042924: Ten goats were set loose in an island and their population growth can be approximated by the function:
p(t)=greatest integer function of [60(t+1)] / (t+6)
where p represents the goat population in year t since they were set loose.
a)how many goats there will be in 5 years?
b)what is the maximum goat population that the island can support?
p.s.
I don't know how to write the greatest integer function sign so i just write it into words. (:
Found 2 solutions by stanbon, ikleyn:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Ten goats were set loose in an island and their population growth can be approximated by the function:
p(t)=greatest integer function of [60(t+1)] / (t+6)
where p represents the goat population in year t since they were set loose.
-----------------------------
a)how many goats there will be in 5 years?
p(5) = [60(5+1)]/(6+6) = [360]/12 = [30] = 30
-----------------------------------------------
b)what is the maximum goat population that the island can support?
As t goes to +oo, p(t) goes to 60t/t = 60
That is the horizontal asymptote and the answer.
Cheers,
Stan H.
-------

Answer by ikleyn(52824) About Me  (Show Source):
You can put this solution on YOUR website!
.
Ten goats were set loose in an island and their population growth can be approximated by the function:
p(t)=greatest integer function of [60(t+1)] / (t+6)
where p represents the goat population in year t since they were set loose.
a) how many goats there will be in 5 years?
b) what is the maximum goat population that the island can support?
p.s.
I don't know how to write the greatest integer function sign so i just write it into words. (:
~~~~~~~~~~~~~~~~~~~~~~ 

a)  how many goats there will be in 5 years?         Calculate %2860%28t%2B1%29%29%2F%28t%2B6%29 at t=5: %2860%2A6%29%2F11 = 360%2F11 = 32.7 ...

                                                     Now take greatest integer lesser than 32.7. It is 32, which is your answer.



b) what is the maximum goat population that the island can support?

   The function p(t) has the horizontal asymptote  p(t) = 60.

   You may treat it as the maximum goat population that the island can support.