heyheyhey701
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- Mar 12, 2011
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A 1-compartment model can be used to study the population effects in the Great lakes. We make 2 assumptions:
- The polllutants are being added to a lake at a constant rate i, and that the pollutants and thoroughly mixed into the lake.
- The annual precipitation into the lake matches evaporation, so the flow rate F is also constant.
Let y(t) be the amount of pollutant in the lake and c(t) its concentration at time t.
The differential equation for y in this 1-compartment model is y' = - (f/v) y + i. Simply dividing this by V and recalling that c(t) = y(t)/v, we find that the differential for c is
c' = -(f/v)c + i/v
Solve the first order linear differential equation for the unknown function c(t) using the 7step method, treating F,V, and I as constants. Use the answer to compute teh long range concentration Cinfinity = lim as t approaches infinity of c(t)
- The polllutants are being added to a lake at a constant rate i, and that the pollutants and thoroughly mixed into the lake.
- The annual precipitation into the lake matches evaporation, so the flow rate F is also constant.
Let y(t) be the amount of pollutant in the lake and c(t) its concentration at time t.
The differential equation for y in this 1-compartment model is y' = - (f/v) y + i. Simply dividing this by V and recalling that c(t) = y(t)/v, we find that the differential for c is
c' = -(f/v)c + i/v
Solve the first order linear differential equation for the unknown function c(t) using the 7step method, treating F,V, and I as constants. Use the answer to compute teh long range concentration Cinfinity = lim as t approaches infinity of c(t)