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Question -

The number of bacteria in a certain culture doubles every hour. If therewere 30 bacteria present in the culture originally, how many bacteria will bepresent at the end of 2nd hour, 4th hourand nth hour?



Answer -

Given, the number ofbacteria doubles every hour. Hence, the number of bacteria after every hourwill form a G.P.

Here we have, a =30 and r = 2

So, a3 = ar2 =(30) (2)2 = 120

Thus, the number ofbacteria at the end of 2nd hour will be 120.

And, a5 = ar4 =(30) (2)4 = 480

The number of bacteriaat the end of 4th hour will be 480.

an +1 arn = (30) 2n

Therefore, the numberof bacteria at the end of nth hour will be 30(2)n.

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