Strain of Bacteria

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umaa: Legendary Member; Posts: 727; Joined: Sun Jun 08, 2008 9:32 pmFollowed by: 1 member; Thanked: 8 times

by umaa » Wed Nov 25, 2009 6:21 pm

A strain of bacteria multiples such that the ratio of its population in any two consecutive minutes in constant,
If the bacteria grows from a population of 5 million to a population of 40 million in one hour, by what factor does the population increase every 10 minutes?

OA is sqrroot 2

What we think, we become

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Source: Beat The GMAT — Problem Solving | Wed Nov 25, 2009 6:21 pm

thephoenix: Legendary Member; Posts: 1560; Joined: Tue Nov 17, 2009 2:38 amFollowed by: 5 members; Thanked: 137 times

by thephoenix » Wed Nov 25, 2009 8:04 pm

basically its a GP
start =5*10^6=say x0
after 2min its x0*r(say r as a constant factor)
similarly for 10th min its x0*r^5 we are asked what is r^5and for 6oTh min its x0*r^30=40*10^6

now we know x0=5*10^6

therefore for 60th min x0*r^30=40*10^6
or r^30=40/5=8
which is same as r^5)^6=2^3
solving r^5=sqrroot 2

hence ans is sqrroot2

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Birgit Anne: Junior | Next Rank: 30 Posts; Posts: 13; Joined: Thu Nov 26, 2009 6:51 am

by Birgit Anne » Thu Nov 26, 2009 8:10 am

I understand it until the point r^30=8, but I cannot follow your last two steps.

Can anyone please explain that to me?

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thephoenix: Legendary Member; Posts: 1560; Joined: Tue Nov 17, 2009 2:38 amFollowed by: 5 members; Thanked: 137 times

by thephoenix » Thu Nov 26, 2009 8:42 pm

Birgit Anne wrote:I understand it until the point r^30=8, but I cannot follow your last two steps.

Can anyone please explain that to me?

r^30=8
(r)^(5*6)=2^3
taking sixth root both side
r^5=2^(3/6)
r^5=2^(1/2)=sqrt2
hence r^5=sqrt2

and every tenth minute its inc by factor of r^5 and hence sqrt2

HTH

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adam15: Senior | Next Rank: 100 Posts; Posts: 70; Joined: Mon May 12, 2008 12:26 pm; Thanked: 3 times

by adam15 » Thu Nov 26, 2009 9:18 pm

we know that the ratio between two successive minute is constant thus
let t1 the first minute and t2 second minute...t60
thus
t1/t2=t2/t3=t3/t4=...=t59/t60=r
multiple all terms
t1/t2*t2/t3....*t58/t59*t59/t60=r*r....*r (6o times)
thus
t1/t60=r^60
we know that t1 correspond to 5, and t60 correspond to 40 thus
5/40=2^3
thus r^60=2^3
thus r=2^(1/20)
after 10 minute we will have

r^10=2^(1/2)= square root of 2

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Birgit Anne: Junior | Next Rank: 30 Posts; Posts: 13; Joined: Thu Nov 26, 2009 6:51 am

by Birgit Anne » Fri Nov 27, 2009 12:02 am

Thank you both!

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