ankitaprsd wrote:

If a certain culture of bacteria increases by a factor of x every y minutes, how long will it take for the culture to increase to 10000 times its original amount ?

1) (x)^1/y = 10

2) In 2 minutes the culture will increase to 100 times its original amount.

Please could you explain an how to solve such questions which involves population increasing by certain factors

Stem 1 is interesting..

Consider x=10 and y=1...so Initial bacteria (K) will increase by a factor of 10 in 1 minute...so after 1 minute there will be K+10K=11K...so we can find the time it will take for culture to increase to 10000 times

So after 1 minute, we have 11K

After 2 minutes, 11K+110K=121K

After 3 minutes= 121K+1210K=1331K

After 4 minutes...

Consider \(x=\sqrt{10}\), and y =1/2 or 30 seconds, So after 30 seconds, no. of bacteria will increase by \((10^{1/2})^{2}\) or by a factor of 10...in 1 minute it will increase by factor \(\sqrt{10}\)

At 0 seconds=K

After 30 seconds= K+10K=11K

After 1 minute, by a factor\(\sqrt{10}\) so after 1 minute you will have \(11K+\sqrt{10}*11K\)----->

Now here the problem is the increase every y minute is not the same so this case will not be considered...

So St1 is sufficient

St2 is straight forward...

Can you post the Official Explanation to question.

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