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

Limits, differentiation, related rates, integration, trig integrals, etc.

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

Postby mabasamunashe on Thu Oct 10, 2013 8:57 pm

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?
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Re: [SPLIT, MOVED] A colony of ants brings food to its hive

Postby nona.m.nona on Thu Oct 10, 2013 11:09 pm

mabasamunashe wrote: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?

mabasamunashe wrote: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?
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Re: [SPLIT, MOVED] A colony of ants brings food to its hive

Postby mabasamunashe on Thu Oct 24, 2013 9:30 pm

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.
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Re: [SPLIT, MOVED] A colony of ants brings food to its hive

Postby nona.m.nona on Thu Oct 24, 2013 10:05 pm

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