A common inhabitant of human intestines is the bacterium Escherichia coli.?

Question

A cell of this bacterium in a nutrient-broth medium divides into two cells every 20 minutes. The initial population of a culture is 56 cells.

A.) Find the relative growth rate. k=_____ cells per hour

B.) Find an expression for the number of cells after t hours.

P(t)=_______________

C.) Find the number of cells after 5 hours. =____billion cells

D.) Find the rate of growth after 5 hours. =____billion cells/hr

E.) When will the population reach 20,000 cells? =___hours

Answer 1

Because it divides into two cells every 20 minutes, therefore in one hour it will divide 3 times.

So, if initially we have 56 bacterial cells...the calculation would be as follows after 1 hour.....

56x2=112 bacterial cells after 20 min.

112x2=224 after 40 min

224x2=448 after 1 hour

so, the growth rate K= after 1 hour is equal to 448/56=8 times

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Answer to Q.A

A.) Find the relative growth rate. k=8 times to the initial number at 0 hour =56cells per hour

C)1,835,000 after 5 hours ( it will divide for 15 times in 5 hours...Find beneath, the calculation is  so easy)

FOLLOW the calculation

......56x2=112x2=224x2=448x2=896x2==>>

1792....it is after 5 divisions and you have to do like this till 15 times for a total 5 hours span--->---->15 times x 2 = 1,835,000 cells

D. 1,835,000/initial number56= growth rate after 5 hours = Approx 32768 times

E.  after 8 times of division the number will be approx. 28672 cells............8 times means 8x20minutes=160 minutes= 2 hours and 40 minutes ( but this calculation is a little more than 20,000).

So, you have to calculate or assume a little shorter time about 2 and  a half hours and reduce the amount upto 20,000 cells ( just gross calculation).

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I HAVE GOT TWO GOOD links . You can get there good calculation formula.

PLEASE open the link...

1. Bacterial Growth  

... formula is Ln(P/Po) = k*(t - to) where 'P' is the population at time 't', and ' ... because growth depends on available nutrients, the "death" rate, and so on. ...

http://www.newton.dep.anl.gov/askasci/ma...

2. Exponential growth - Wikipedia, the free encyclopedia  

Basic formula. A quantity x depends ... b = k 0 is the rate of ... by M. G. Dmitriev and A. P. Petrov, pp. 367–9. Moscow: Russian State Social ...

http://en.wikipedia.org/wiki/Exponential...