Applications of Linear Systems with Constant Coefficients 405c. Assume the initial concentration of pollution in each lake is .5%- thatis, assume ci(O) = .005. When will the concentration of pollution in each lake
be reduced to .4%? .3%? (HINT: Solve the initial value problem: c' =Ac;
ci(O) = .005. Then graph the equation for the concentration of pollution in
each lake and determine when the concentration drops below the specified
levels.)
d. Assume the con centration of pollution entering the Great Lakes from
outside the system is reduced from the current levels to .2%- that is, assume
Cs = Cm = C1i = Ce = Co = .002.
(i) Find the general solution of c' = Ac + b. (HINT: Assume there is a
particular solution, Cp, in which each component is a constant. The general
solution is c = C c + Cp where C c is the answer to part b .)
(ii) Now assume the initial concentration of pollution in each la ke is ci(O) =1 % = .01. When will t he concentration of pollution in each lake be reduced
to .53? .3%? (HINT: Solve the initial value problem: c' =Ac+ b; ci(O) =
.01. Then graph the equation for t he concentration of pollution in each lake
and determine when the co ncentration of pollution drops below the specified
levels.)