A bacteria culture starts with 500 bacteria and doubles in size every 6 hours. How do you find an exponential model for t?

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Answer 1 · 2017-09-25T12:34:27

Exponential model of bacteria growth at time #t# is
#B_t= 500 *e^(0.115525t)#

Starting number of bacteria is # B_0 = 500 # , It doubles in

size every #6# hours. Number of bacteria after #t=6# hours

grows to # B_6=B_0*2=500*2=1000 #. The exponential growth

formula is # B_t= B_0 *e ^(kt)# , where #k# is growth rate

# :. e^(kt) = B_t/B_0 or e^(kt) = 1000/500=2 # Taking natural

log on both sides we get # ln e^(kt) = ln 2 or kt= ln 2 # (since

#ln e^(kt)=kt#) # :. k =ln2/t=ln 2/6 or k ~~ 0.115525#

Exponential model of bacteria growth at time #t# is

#B_t= 500 *e^(0.115525t)# [Ans]