58. The population p(t) at time t of a certain mouse species satisfies the differential equation =0.5 p(t) — 450. If p(0) = 850, then the time at which the population becomes zero is:

(1) (2) ln 18 (3) 2 ln 18 (4) ln 9

Sol. (3)

P — 900 = k.et/2

P(0) = 850

— 50 = k k = — 50

If p = 0

–900 = — 50 et/2 t = 2 ln 18.