bacteria???

Question

A certain colony of bacteria grows at a rate proportional to the number of bacteria present. Suppose the number of bacteria doubles every 12 hours. How long (in hours) will it take this colony to grow to five times its original size?

Time needed = _________ hours

PS
the answer is NOT 27
and is NOT 30 :]

Answer 1

FV = P(1 + r)^t

FV = future value, P = initial value, r = rate of growth, and t = time

We want to know the value of t where FV = 5P, or:

5 = (1+r)^t

But we have two unknowns, so we need to find r. We know:

FV = 2P when t = 12, so:

2 = 1(1+r)^12
2 = (1+r)^12
r = 0.0595 = 5.95%

Now, put this in our equation:

5 = (1.0595)^t
log5 = t*log1.0595
t = log5/log1.0595
t = 27.85 hours

Hope this helps!

Answer 2

I'm not sure if this answer is right, but the way i did it, the answer is 48 hrs.

This is how I got it-

say number of present bacteria= B,

then dB/dt is proportional to B

now applying a proportionality constant k, we can say

dB/dt= kB

we know that B becomes 2B in 12 hrs.

Therefore, dB= 2B-B=B

Therefore B/12= kB, i.e, k=1/12

Now, dB/dt= (1/12)B

Now for 5 times its original size,

dB= 4B.

Therefore, 4B= (1/12) B*dt
which gives dt= 48 hrs

I hope this is right.

Answer 3

"large fleas have little fleas upon their backs to bite 'em, And little fleas have lesser fleas, and so ad infinitum. And the whole fleas themselves, in turn, have better fleas to flow on, at the same time as those back have better nevertheless, and bigger nevertheless, etc." - Augustus De Morgan, funds of Paradoxes (1872). yet to respond to your question - some micro organism *do* "parasitise" or prey on different micro organism. This in a lot of circumstances takes the kind of the first bacterium generating a toxin which kills off different (rival) micro organism interior the encompassing section - in reality, various commercial antibiotics were got here upon from this source. that is likewise why (as an instance) yoghurt keeps linger than milk - the (danger free) micro organism that inhabit the yoghurt ward off different (risky) micro organism from growing to be there.

Answer 4

N = Noe^kt
2 = e^(12k)
12k = ln 2
k = ln(2)/12 = .0578
N = Noe^.0578t
5 = e^.0578t
t = ln(5)/.0578 = 27.84 hours