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Suppose there are 30 bacteria in a bottle .the number of bacteria doubles every hour.

how many will there be after 7 hours?

1 Answer

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is given that the number of bacteria doubles every hour.

Therefore, the number of bacteria after every hour will form a G.P.

with first term (a=30) and common ratio (r=2)

∴a

3

=ar

2

=(30)(2)

2

=120

Therefore, the number of bacteria at the end of 2nd hour will be 480.

a

5

=ar

4

=(30)(2)

4

=480

and a

n+1

=ar

n

=(30)(2)

n

Thus the number of bacteria at the end of nth hour will be (30)(2)

n

User Dan Kendall
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