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?