the population of iguanas introduced into an isolated island is given by:
P (t)= 72/9-t, 0<t <9 t is months

1.Find the number of iguanas present in the island initially
2.Show that the population of iguanas is increasing without bound

Thanks

you miswrote the function. use parenthesis.
with that said, i'm not sure how to find the initial population since the domain of the function doesn't contain zero.

Kind of a weird population growth formula. As you get closer and closer to midnight on the last day of the 8th month, there will be billions of iguanas birthed every microsecond.

1. P(0) = 72/9 = 8 iguanas
2. What does bound mean? My english is not that good jaja. But it is evident that the function is continous for all t<9 since it is discontinous when 9-t=0 => for t=9, but 0<t<9 for all t.

This post was edited by globo_killer on Nov 6 2015 07:51pm

P(0) is not in the domain.

it means it's always increasing to infinity

it's not, but lim [t->0] p(t) = 72/(9-0) = 8 . t is never 0, but it is still 8 iguanas when t is very small.

Also, for the second part, u can derivate p(t) to obtain p'(t)=72/(9-t)^2 , then the pending of p(t) is always positive for 0<t<9, which means it's always increasing.

This post was edited by globo_killer on Nov 7 2015 10:44am

That's not sufficient. Take -1/t for t > 0. The derivative is 1/(t^2), which is always positive for t > 0, and the function IS always increasing, but it is bounded and will never be more than 0. For a bounded domain like his, even something as simple as P(t) = t has a range bound.
You'd have to take the limit as t->9 and show that P(t) tends to infinity, I would say.

Kinda stupid that they didn't include time 0 in the domain, but other than taking the limit I don't see any reasonable way of answering 1.

This post was edited by russian on Nov 7 2015 02:19pm

Just based on the fact that he didn't include ( ) around the denominator, I'm willing to bet that the domain includes 0 and he just didn't type it out correctly..

1. P(0) = 72/9 = 8

2. lim(P(t),t->9) = +oo


This