Expert: Sherman D. - 4/20/2005

Question
The question is:  
The number of bacteria in a petri dish culture after t hours is  
B= 100e^(0.693t)

a) What was the initial number of bacteria present?
b) How many bacteria are present after 6 hours?
c) Appoximately when will the number of bacteria be 200? Estimiate the doubling time of the bacteria.


Okay, so I am terrible at Calc. Once I learn the procedures, I understand how the quesiton is solved and can do it again. The book just doesn't give great examples. Part of my problem is that I haven't done this stuff in 12 years. I am trying to learn again so I can go back for a masters.

Thanks!

Answer
You ever done Continous Compound Interest
The formula for that is
A = Pe^rt

Look familier, lol.

A = Interest
P = Initial Amount
r = rate
t = time

same thing, only the letters stand for different things

B = 100e^(.693t)

a.) 100 bacteria

b.)
B = 100e^(.693(6))
B = 100e^(4.158)
B = 100 * 63.94350761
B = 6394.350761
or
B = about 6394 bacteria

c.)
200 = 100e^(.693t)
2 = e^(.693t)
log(.693t)2 = e
(log(2))/(log(e)) = .693t
.69314718 = .693t
t = 1.000212382 hours