#### Question

The number of bacteria in a certain culture doubles every hour. If there were 30 bacteria present in the culture originally, how many bacteria will be present at the end of 2^{nd} hour, 4^{th} hour and *n*^{th}hour?

#### Solution

It is given that the number of bacteria doubles every hour. Therefore, the number of bacteria after every hour will form a G.P.

Here, *a* = 30 and *r* = 2

∴ *a*_{3} = *ar*^{2} = (30) (2)^{2} = 120

Therefore, the number of bacteria at the end of 2^{nd} hour will be 120.

*a*_{5} = *ar*^{4} = (30) (2)^{4} = 480

The number of bacteria at the end of 4^{th} hour will be 480.

*a*_{n}_{ +1 }= *ar** ^{n}* = (30) 2

^{n}

Thus, number of bacteria at the end of *n*^{th} hour will be 30(2)^{n}.

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Solution The Number of Bacteria in a Certain Culture Doubles Every Hour. If There Were 30 Bacteria Present in the Culture Originally, How Many Bacteria Will Be Present at the End of 2nd Hour, 4th Hour and Nth Hour? Concept: Relationship Between A.M. and G.M..