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Algebraic way to solve a word problem...

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Algebraic way to solve a word problem...

by topspin330 » Mon Jan 23, 2012 10:07 pm
Can anyone show how to solve this using algebra. Already know how to do it by plugging in numbers.

The population of a certain type of bacterium triples every 10 minutes. If the population of a colony 20 minutes ago was 100, in approximately how many minutes from now will the bacteria population reach 24,000?

It seems like this problem could be structures into y = 3x format don't know how to finish it off.

Thanks.
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by Anurag@Gurome » Mon Jan 23, 2012 10:22 pm
topspin330 wrote:The population of a certain type of bacterium triples every 10 minutes. If the population of a colony 20 minutes ago was 100, in approximately how many minutes from now will the bacteria population reach 24,000?
Say, initial population is x.
After 10 minutes the population will be 3*x.
After 20 minutes the population will be 3*3*x = (3^2)*x.
After 30 minutes the population will be 3*3*3*x = (3^3)*x.
...
After 10*n minutes the population will be (3^n)*x.

Now, x = 100 and final population is 24,000

So, (3^n)*(100) = 24,000
--> (3^n) = 240

Now, we know that 3^5 = 243, hence n ≈ 5.

Hence, after 5*10 = 50 minutes the population will reach 24,000 from an initial population of 100. Out of this 50 minutes, 20 minutes is already passed. Hence, after 30 minutes the population will reach 24,000.
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by pemdas » Mon Jan 23, 2012 10:43 pm
simple way
20 minutes ago -> 100 bacteria
Now -> 100*3*3=900 bacteria
900*3=2700 10 minutes from now
2700*3=8100 20 minutes from now
8100*3>24000 30 minutes from now

exponential growth way
20+t=n*10 and 100*3^n>=24000, 3^n>=240 and n>=5, n should be minimum 5
t=50-20=30 minutes
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by LalaB » Mon Jan 23, 2012 11:53 pm
topspin330 wrote:Can anyone show how to solve this using algebra. Already know how to do it by plugging in numbers.

The population of a certain type of bacterium triples every 10 minutes. If the population of a colony 20 minutes ago was 100, in approximately how many minutes from now will the bacteria population reach 24,000?

It seems like this problem could be structures into y = 3x format don't know how to finish it off.

Thanks.
please refer to MGMAT Word translation 4th edition pages 44 and 174.

or else see below :)
now=100*3^(20/10)=100*9=900

24000=900*3^t/10
27=3^t/10
t=30

hence after 30 mins everything will be ok :)
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