Assume that Lake Erie has a volume of 480 km3 and that its rates of inflow (from Lake Huron) and outflow (to Lake Ontario) are both 350km2 per year. Suppose that at the time t=0 (in years), the pollutant concentration of Lake Erie - caused by past industrial pollution that has now been ordered to cease - is five times that of Lake Huron. If the outflow from Lake Erie henceforth is perfectly mixed lake water, how long will it take to reduce the pollution concentration in Lake Erie to twice that of Lake Huron? How to solve this problem?

Question

anonymous · Answer

What class is this for?

anonymous · Answer

Caculus

anonymous · Answer

This problem is the application of solving implicit differential equation but I have no idea how to do this problem

anonymous · Answer

i believe it's (rate in - rate out) and you create a differential equation from it

anonymous · Answer

i haven't done these in awhile and forgot the formula but we know that

V(erie)=480km^3     rate(in)=350km^2/yr  rate(out)=350km^2/yr
P(0)=5(Huron) P(t)=2(Huron)

anonymous · Answer

right, but i wonder since the rate(in) and rate(out) the same, the change in the total volume is the same right?

anonymous · Answer

and i stuck at the part on how to get out the equation of the pollutant concentration?

anonymous · Answer

i figured it out; you're trying to find the rate at which pollution is going out so that you can get a function which gives you the amount of pollution in the lake... 

you need dp/dt 

dp/dt = (pollution in - pollution out)
dp/dt = .2(35/48)-35p/48

differentiate

anonymous · Answer

you get it?

anonymous · Answer

Hm. Thanks for your help!

anonymous · Answer

why is it .2(35/48)? why is it .2?

anonymous · Answer

well the rate in is the water from lake huron to eerie. since lake huron is 5 times less polluted than the water in lake eerie. you can say that water is 1/5 as polluted as the lake eerie water.