## [SPLIT, MOVED] A colony of ants brings food to its hive at....

Limits, differentiation, related rates, integration, trig integrals, etc.
mabasamunashe
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### [SPLIT, MOVED] A colony of ants brings food to its hive at....

A colony of ants brings food to its hive at a constant rate of 500grammes per day.It consumes food at a rate of (x/2)grammes per day,where x is the amount of food present at time t days.taking x and t to be continuos variables write down a diffrential equition Ssatisfied by x andt to show the rate at which food is increasing in the hive.

i have said dx/dt=(inflow-outflow)/total amount available
that is dx/dt=(500-x/2)/x
is this correct?

nona.m.nona
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Joined: Sun Dec 14, 2008 11:07 pm
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### Re: [SPLIT, MOVED] A colony of ants brings food to its hive

A colony of ants brings food to its hive at a constant rate of 500grammes per day.It consumes food at a rate of (x/2)grammes per day,where x is the amount of food present at time t days.taking x and t to be continuos variables write down a diffrential equition Ssatisfied by x andt to show the rate at which food is increasing in the hive.

i have said dx/dt=(inflow-outflow)/total amount available
Would not "total amount available" be, by definition, equal to "inflow, less outflow"? Therefore, what is the distinction between your numerator and your denominator above?
that is dx/dt=(500-x/2)/x
This simplifies as dx/dt = (500/x) - (1/2). How does this relate to the posted exercise?

mabasamunashe
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Joined: Thu Oct 10, 2013 7:18 pm
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### Re: [SPLIT, MOVED] A colony of ants brings food to its hive

please help me how to come out with the solution for the diffrential i'm failing to come up with the solution i tried it so many times but yeah! it made me puff.I don't have anybody to ask i'm doing A-level maths withot the aid of a teacher.

nona.m.nona
Posts: 288
Joined: Sun Dec 14, 2008 11:07 pm
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### Re: [SPLIT, MOVED] A colony of ants brings food to its hive

What solution have you been given? How does your work compare with the general thinking behind, for instance, the "Population" example on this page?