Question

Fruit flies are placed in a half-pint milk bottle with a banana (for food) and yeast plants (for food and to provide a stimulus to lay eggs). Suppose that the fruit fly population after t days is given by:

Answer 1

\[p(t)=\frac{ 230 }{ 1+56.5e ^{-0.37t} }\] What is the carrying capacity of the half pint bottle? (i.e, What is p(t) as t approaches ∞?)

Answer 2

those question marks represent infinity. i don't know why it didn't show

Answer 3

what does e^-infinity represent

Answer 4

what do you mean?

Answer 5

230

Answer 6

can you briefly explain?

Answer 7

P(t) would be 230 as t approaches infinite

Answer 8

because my teacher told me we have to write like a little paragraph on explaining it.

Answer 9

yeah i can, see when t tends to infinity the denominator becomes 1 as, 56.5e^-0.37t would be zero

Answer 10

wait so how does that prove that the carrying capacity is 230?

Answer 11

the same thing is asked in the question? the value of P at t=infinite.

Answer 12

right

Answer 13

I'm sorry I'm confused...

Answer 14

you want
lim(t->oo) 230 / ( 1 + 56.5 * e^ (-.37*t)

Answer 15

why see at t=0 the value is 4

Answer 16

so 4 is the initial amount of fruit flies? how does that help

Answer 17

and the fruit flies will occupy the whole bottle. they will not grow when the no banana is left

Answer 18

there is banana in the half pint bottle and fruit flies grow with the function given. they will grow till they have eaten whole banana.

Answer 19

lim(t->oo) 230 / ( 1 + 56.5 * e^ (-.37*t)
= 230 / ( 1 + 56.5 * e^(-.37 * oo)
= 230 / ( 1 + 56.5 *0)
=230/(1 + 0)
=230

Answer 20

assumption that at t=infinity they must have consumed whole banana and ability to multiply again will be finished

Answer 21

this would be my set of explanation for this problem.

Answer 22

the question is not asking about the banana, it is asking the total population of fruit flies

Answer 23

but youre right, they would probably eat the banana and the yeast

Answer 24

:)