Question

As the breeding season progresses, penguin parents have to devote a bigger proportion of their catch
to feed their chicks, until they fledge and are able to feed by themselves. The following equation
describes this phenomenon, where P is the proportion of prey given to chicks and t is time in weeks
over the course of the breeding season: P(t) = 100t^2/(200+t^2).
Do you think P(t) adquately describes penguin feeding behavior over the course of a penguin's life? Explain your answer based on the equation given.

Answer 1

It won't, since P(t) ultimately exceeds one as t grows

Answer 2

wait

Answer 3

That seems about right, but doesn't long term behavior suggest that P(t) = 1

Answer 4

whats the life duration of a penguin

Answer 5

I mean approaches 1

Answer 6

Either way, I don't thinnk it's proportional

Answer 7

right P(t) goes to 1

Answer 8

P(T) does not exceed one, who said that?

Answer 9

it eventually does exceed one.

Answer 10

no it never does

Answer 11

it does. :-P

Answer 12

http://www.wolframalpha.com/input/?i=100t%5E2%2F%28200%2Bt%5E2%29

Answer 13

But the fact that it approaches one would be a good enough reason to say it doesn't sufficiently model pengiun stuff

Answer 14

weird, i divided both top and bottom by t^2 and found the limit as t approaches infinity

Answer 15

it's 100, right?

Answer 16

right

Answer 17

remember P(t) is percent

Answer 18

its a percent.... I forgot that totally :-P

Answer 19

well, it does exceed one... one percent

Answer 20

100% = 1

Answer 21

right , so is it now reasonable?

Answer 22

well at first it is true, but then the chick grows up and does not need food anymore, so this equation is not true for large t

Answer 23

how long is a penguin chick raising ?