SOLUTION: A culture of bacteria triples after 7 hours. (a) What proportion of the original number of bacteria Q0 will be present after 14 hours? Q(14) = (b) What proportion of the ori

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: A culture of bacteria triples after 7 hours. (a) What proportion of the original number of bacteria Q0 will be present after 14 hours? Q(14) = (b) What proportion of the ori      Log On

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Question 953958: A culture of bacteria triples after 7 hours.
(a) What proportion of the original number of bacteria Q0 will be present after 14 hours?
Q(14) =
(b) What proportion of the original number of bacteria Q0 will be present after 28 hours?
Q(28) =

Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
Exponential growth model, y=p%2Ae%5E%28kt%29.

The description indicates
ln%28y%29=ln%28p%29%2Bkt
kt=ln%28y%29-ln%28p%29
kt=ln%28y%2Fp%29
k=ln%28y%2Fp%29%2Ft
k=ln%283%2F1%29%2F7
highlight_green%28k=ln%283%29%2F7%29
The decimal approximation for this is highlight_green%28k=0.157%29.

Growth Model can be stated, y=p%2Ae%5E%280.157t%29.

You could take as general starting point, p=1 for ALL of any original amount of bacteria; when 14 hours pass, y%2814%29=1%2Ae%5E%280.157%2A14%29, and you already were given that y%287%29=1%2Ae%5E%280.157%2A7%29=3.
Question (a) means, what is 1%2F%28y%2814%29%29. You want as percentage.

Find that y(14)=9 which makes sense because you knew that 7 hours was the amount of time to triple in size.