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An initial number of bacteria presented ...

An initial number of bacteria presented in a culture is 10000. This number doubles every 30 minutes. How long will it take to bacteria to reach the number 100000 ?

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The correct Answer is:
100 minutes
Initially bacteria count is 10000.
After 30 min. it doubles i.e., ` 2xx 10000`.
After 60 min. it is`2^(2) xx 10000`.
So, after t minutes, bacteria count will be ` N = 10000 xx 2^(t/30)`
For ` N = 100000`,we have
`100000 = 10000 xx 2^(t/30)`
` :. 2^(t/30) = 10`
` t/30 log_(10) 2 = 1`
` rArr t = (30)/(log_(10) 2) = 30/(0.301) = 99. 67`
So, it will take approximately 100 minutes.
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