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bacterial growth

by gunjan1208 » Thu Sep 22, 2011 9:20 pm
A strain of bacteria multiplies such that the ratio of its population in any two
consecutive minutes is 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 after some explanations....

Source: Manhattan strategy guide
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by rohit_gmat » Thu Sep 22, 2011 9:35 pm
gunjan1208 wrote:A strain of bacteria multiplies such that the ratio of its population in any two
consecutive minutes is 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 after some explanations....

Source: Manhattan strategy guide
woow... do u have AC?... i have no idea whether wat i did below is correct or not :P

5 mil -> 40 mil (x 8) in 1 hour

8 = x^60 (x = factor inc per min)
x = 8 ^ (1/60)
10 mins = x^10 = 8^(1/6) = 8^(1/3)(1/2) = 2^(1/2) = sqrt2

so the factor inc in 10 mins wud be sqrt 2.... :S
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by knight247 » Thu Sep 22, 2011 9:39 pm
y0=5,000,000
y60=40,000,000
Number of change intervals=6 as in the span on 60 minutes there would be 6 intervals of 10 minutes each

We use the formula
y(t)=y0*k^t

Plugging in the values in this equation we have
40,000,000=5,000,000*k^6
k^6=8
k^6=2^3
k=6th root of 2^3
k=√2
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by gunjan1208 » Thu Sep 22, 2011 10:53 pm
Hi Both,

Great. You nailed it. Absolutely it is sqrt(2)

Knight: I liked your way to do it....Its the way explained in Manhattan. At the same time answer by Rohit is very short and logical.

In fact in the morning I was confused by the way square root solution is explained in Manhattan. But Knight, you gave me a solution. Thanks.
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by GMATGuruNY » Thu Sep 22, 2011 11:32 pm
I posted a solution here:

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by saketk » Thu Sep 22, 2011 11:43 pm
Ratio is constant, that means it's a GP.

first term a =5
last term ar^6=40

or r^6=8
r= srt(2)
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