# First ODE (dc/dt the rate of change of chemical in a pond)

hangainlover
lets say there is a pond of 1,000,000 gallons of water.
and the total of 10,000g of chemical is evenly dissolved in the water
Fresh water starts pouring into the pond at the rate of 300 gallons/hour and the pond also releases water at the rate of 300 gallons/hour (hence no change in total amount in the pond).
Can you set up a differential equation describing the rate of change of the chemical in the pond. (dc/dt)
(I know that dC/dt = (the total amount of the chemical in the pond at a given time / 1,000,000 gallons of waer)*300 gallons/3600seconds) but i cant define the total amount of chemcial left in the pond at a given time, as the total amount doesnt change linearly or by a pattern i can see )

## Answers and Replies

Staff Emeritus
Homework Helper
lets say there is a pond of 1,000,000 gallons of water.
and the total of 10,000g of chemical is evenly dissolved in the water
Fresh water starts pouring into the pond at the rate of 300 gallons/hour and the pond also releases water at the rate of 300 gallons/hour (hence no change in total amount in the pond).
Can you set up a differential equation describing the rate of change of the chemical in the pond. (dc/dt)
(I know that dC/dt = (the total amount of the chemical in the pond at a given time / 1,000,000 gallons of waer)*300 gallons/3600seconds) but i cant define the total amount of chemcial left in the pond at a given time, as the total amount doesnt change linearly or by a pattern i can see )

But you have pretty much already defined it. "The total amount of chemical in the pond at a given time" is C, or if you prefer C(t).

Also, since the problem statement uses hours as the unit of time, you might as well keep time in terms of hours rather than converting to seconds.

hangainlover
omg im so stupid how did i miss that
thanks

Staff Emeritus
No problem! 