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Question Number 63424 by Rio Michael last updated on 04/Jul/19

A c o l o n y o f b a c t e r i a i f l e f t u n d i s t u r b e d w i l l g r o w a t a r a t e

p r o p o r t i o n a l t o t h e n u m b e r o f b a c t e r i a, P p r e s e n t a t t i m e, t .

H o w e v e r, a t o x i c s u b s t a n c e i s b e i n g a d d e d s l o w l y s u c h t h a t

a t t i m e t, t h e b a c t e r i a a l s o d i e a t t h e r a t e μ P t w h e r e μ i s

a p o s i t i v e c o n s t a n t .

(a) S h o w t h a t a t t i m e t t h e r a t e o f g r o w t h o f t h e b a c t e r i a i n

t h e c o l o n y i s g o v e r n e d b y t h e d i f f e r e n t i a l e q u a t i o n

\frac{d P}{d t} = (k - μ t) p w h e r e k i s a p o s i t i v e c o n s t a n t .

w h e n t = 0, \frac{d P}{d t} = 2 P a n d w h e n t = 1, \frac{d P}{d t} = \frac{19}{10} P

(b) s h o w t h a t

\frac{d P}{d t} = \frac{1}{10} (20 - t) P .

S i r F o r k u m M i c h a e l .