A bacteria culture initially contains 1500 bacteria and doubles every half hour. The formula for the population is p(t)= 1500e^kt for some constant k, how do you find the size of the population after 60 minutes?

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Answer 1 · 2017-11-05T12:52:03

Bacteria population after #60# minutes is #6000#

#1500# bacteria doubles to #1500*2=3000# in #30# minutes

#3000# bacteria doubles to #3000*2=6000# in

next #30# minutes . i.e in #60# minutes.

General procedure for any time required:

#p(t)= 1500 e^(kt) (1) ; :. p(0)= 1500*e^0=1500 (1)# and

#:p(30)= 1500e^(30k);(2) =3000# . Dividing equation (2) by

equation (1) we get # (p(30))/(p(0))#

#=(1500e^(30k))/(1500*e^0)=3000/1500 or e^(30k)=2#

Taking natural log on both sides we get

#30k ln e =ln2 or k= ln2/30=0.023105 [lne=1]#

Bacteria population after #t=60# minutes is

#p(60)= 1500 e^(0.23105*60)= 6000# [Ans]