Problem 3 100 lbs of a toxic substance were spilled into Lake A. Over time it was carried downstream into Lakes B and C successively. Let a(t), b(t), c(t) be the amount of pollutant in each lake at the t-th [a(t) ] week (so a(0) = 100, b(0) = c(0) = 0), and let i(t) = b(t) . Suppose that c(t) ] 0.7 0 0 i(t + 1) = 0.1 0.6 0 I(t). 0 0.2 0.8 Find a closed-form expression for each of a(t), b(t), c(t). (Hint: the eigenvalues of a lower triangular matrix are the diagonal entries.)