1 more...sorry

[Daniel_Feldman]

Either my math abilities are diminishing or I just need to sleep, but as always, help would be great. I'm stuck. Thinking about separation of variables....


A pack of ants is eating Steve's bagel (1200 grams) at a rate proportional to 1/12 of the amount present. When half of the bagel is eaten,, a pack of cockroaches join the ants and the eating continues at a rate proportional to 25% of the amount present. When will Steve's bagel be the proper size for him to eat (185 grams)?

Note: The rates in this problem are per day.

 

[Gene]

B₀ = 600
dB/dt = -.25B
dB/B = -.25dt
ln(B)=ln(e^(-.25t)+ln(B₀)
B=B₀e^(-.25t)

(I think)

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Gene

 

[Daniel_Feldman]

B₀ = 600
dB/dt = -.25B
dB/B = -.25dt
ln(B)=ln(e^(-.25t)+ln(B₀)
B=B₀e^(-.25t)

(I think)

------------
Gene

Thanks....and I do the same thing from 1200 to 600.

 

[Unco]

Perhaps the question's wording is a little dodgy.

\(\displaystyle \L \mbox{ \frac{dm}{dt} \alpha \frac{m}{12} \Rightarrow \frac{dm}{dt} = \frac{Am}{12} = Bm}\)

where \(\displaystyle \mbox{A}\) is some constant and \(\displaystyle \mbox{B = \frac{A}{12}}\).

That is to say, the constant takes care of direct proportionality.

 

[Gene]

I do have some question as to whether it is 1/4 or 1/3 when both are nibbling.
------------------
Gene

 

[Unco]

Your interpretation, which I do not doubt to be that which is intended, is that "at a rate proportional to 1/12 of the amount present" is actually "at a rate equal to 1/12 of the amount present at that instant".

 

[stapel]

"...a pack of cockroaches join the ants and the eating continues at a rate proportional to 25% of the amount present...."

I do have some question as to whether it is 1/4 or 1/3 when both are nibbling.

I took this to mean that the 25% was the sum of the damage done by all the bugs.

Eliz.

 

[Gene]

That's what I settled on but my flabber would not be gasted if Dan'l came back with "the book says 1/3, you clod!" An author who would eat a two week old, roach covered bagel is capable of anything :evil:
----------------
Gene

 

[Daniel_Feldman]

That's what I settled on but my flabber would not be gasted if Dan'l came back with "the book says 1/3, you clod!" An author who would eat a two week old, roach covered bagel is capable of anything :evil:
----------------
Gene

Your answer was right (for 600 to 185 >> I added the same thing from 1200 to 600). Thanks again for your help.