SOLUTION: A bacteria culture starts with 360 bacteria and grows at a rate proportional to its size. After 2 hours there will be 720 bacteria. (a) Express the population after t hours as

Question 1136373: A bacteria culture starts with 360 bacteria and grows at a rate proportional to its size. After 2 hours there will be 720 bacteria.
(a) Express the population after t hours as a function of t.
population:
(function of t)
(b) What will be the population after 9 hours?

(c) How long will it take for the population to reach 2810 ?

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
P=Ab^t, t is hours and P is total and A is beginning
720=360*b^2
b^2=2
b= sqrt (2)=1.414. P=360* sqrt(2)^t
After 9 hours it would be 360*b^9=8134.81 or 8135.
To reach 2880, this would be doubling three times so a little fewer than 6 hours to reach 2810
Mathematically, 2810=360*sqrt(2)^n
7.81=sqrt(2)^n
ln both sides
2.05=n *0.3466
rounding at end 5.93 hours.

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