I need a bit of help with this question:
'A polluted river with a nutrient concentration of 90g.m^3 is flowing at a rate of 100m^3/day into an estuary of volume 1000m^3. At the same time, water from the estuary is flowing into the ocean at 100m^3/day. The initial nutrient concentration in the estuary is 20g/min^3.
(i) Let N(t) be the amount of nutrient (in grams) in the estuary at time t. Write down and slove an appropriate differential equation for N(t) along with the appropriate initial condition.'
My workings have got me this far:
N'(t)=(rate of nutrient going in)-(rate of nutrient going out)=((N(t)g nutrient)/1000m^3)-(100m^3/days)=(N(t)g of nutrient)/((10+t)days)
I think the differential equation should be along the lines of:
N'(t)=9000-(N(t)/(10+t)) => N'(t)+N(t)/(10+t)=9000
but I'm really not too sure. Should that be the end of the equation, or have I missed a few steps?