Find the relative growth rate. (Assume t is measured in hours.)

Question

luigi0210 · Answer

A common inhabitant of human intestines is the bacterium $Escherichia~coli$. A cell of this bacterium in a nutrient-broth medium divides into two cells every 20 minutes. The initial population of a culture is 64 cells.

anonymous · Answer

do you know the formula?

rock_mit182 · Answer

$$y = 60 t ^{\frac{ 1 }{ 3 }}$$

rock_mit182 · Answer

i mean the initial would be 64

luigi0210 · Answer

Nope, I don't know it.. totally new and haven't been taught it yet.
And you sure? So the the initial is 64?

solomonzelman · Answer

that's what your q states (at least)

solomonzelman · Answer

Am I good at googling ? http://answers.yahoo.com/question/index?qid=20080316183032AA2lJBD

ikram002p · Answer

well its clear if t is the time then 
at t_0=0 f(0)=64
at t(20) 
f(20)=64^2
and so on ...

rock_mit182 · Answer

20 minutes is $$\frac{ 1 }{ 3 }$$ of a hour

rock_mit182 · Answer

but im not completly sure about the exponent, it could be . .

luigi0210 · Answer

@SolomonZelman You're good at googling but the answers are wrong xD

ikram002p · Answer

hmm so the population f(t) would be
$\large f(t)=f(0)e^{kt}$
f(0)=64
hmm as t in hour so yes its 1/3 for 20 min
now we need to find k using
$\large f(1/3)=64 * e^{1/3k}$
ohh and f(1/3)=64*2 (not as i mintioned before )
solve for k
so u would have the population function
 and the relative growth rate would be  k !

anonymous · Answer

Formula
A = P (2)^(t/h)

A = final population
P = initial population
t = time
h = time it takes to double

In this case, A = 64(2)^(t/20), where t is in minutes

ikram002p · Answer

and what is  the the relative growth rate @sourwing  :o

anonymous · Answer

set e^r = 2^(1/20) and solve for r

anonymous · Answer

r = 0.03465 or 3.465%. 

relative rate in different time unit will certainly be different.

anonymous · Answer

in hours,rate is

e^r = e^(1/(20/60))
r = 0.23105 or 23.105%

anonymous · Answer

typo, it's e^r = 2^(1/(20/60))

anonymous · Answer

relative rate is still correct

ikram002p · Answer

ive got 
2.079 
hmm idk maby there is somthing wrong with my answer

anonymous · Answer

opps. the equation was right, i did the math wrong :DD

e^r =  2^(1/(20/60)), then r = 2.079 %

ikram002p · Answer

so were both are correct ^_^

anonymous · Answer

yep ^.-b

ikram002p · Answer

:D

luigi0210 · Answer

Tried following along and makes sense now, thanks guys :D