SOLUTION: A certain culture of the bacterium Rhodobacter sphaeroides initially has 40 bacteria and is observed to double every 6 hours.
(a) Find an exponential model
n(t) = n02t/a
for t
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Question 1157132: A certain culture of the bacterium Rhodobacter sphaeroides initially has 40 bacteria and is observed to double every 6 hours.
(a) Find an exponential model
n(t) = n02t/a
for the number of bacteria in the culture after t hours.
n(t) =___________
(b) Estimate the number of bacteria after 15 hours. (Round your answer to the nearest whole number.)
______bacteria
(c) After how many hours will the bacteria count reach 1 million? (Round your answer to one decimal place.)
t = ________hr
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
n(t)=no (1+r)^x
n(t)=40(1+r)^x
80=40(1+r)^6
2=(1+r)^6
ln 2=6 ln (1+r)
ln2/6=0.0155=1n(1+r)
raise to e power
1.122=1+r
r=12.2% growth rate per hour.
after t hours, n(t)=40(1.122)^t
after 15 hours n(15)=40*5.622=224.88 or 225, start rounding at the end. 80 at 6 hours 160 at 12 and 320 at 18 so reasonable answer
1000000=40(1.122)^t
25000=1.122^t
ln 25000=t ln 1.122
divide through
t=87.97 or 88.0 hours
rough check
1 million / 40=25000
2^14=16384
2^15=32768
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