5. A population P of bacteria grows at a rate (say b.P , b > 0) proportional to its size, but it is destroyed at a stead

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5 A Population P Of Bacteria Grows At A Rate Say B P B 0 Proportional To Its Size But It Is Destroyed At A Stead 1 (76.39 KiB) Viewed 66 times

5. A population P of bacteria grows at a rate (say b.P , b > 0) proportional to its size, but it is destroyed at a steadily increasing rate (say cit, c > 0) by a spot of mold which starts growing at t = 0. Under what circumstances will the mold completely consume the bacteria ? Hint. Solve P' (t) = bP(t) – ct in terms of b, c, P(0) and t. Under what condition(s) (on P(0), b and c) will P(t) drop to zero for some t > 0 ?