# The number

Given: there were 30 bacteria present originally and culture doubles every hour.

a0 = 30

After an hour culture is a0 × 2 = 30 × 2 = 60

Since the count doubles every hour it forms a G.P. with r = 2

Let the G.P be a0,a1r,a2r2........

The culture at the end of 2nd hour = ar2 = 30 × 22 = 120

The culture at the end of 4th hour = ar4 = 30 × 24 = 480

The culture at the end of nth hour = arn = 30 × 2n

Culture at end pf 2nd , 4th , nth hours are 120, 480, 30 × 2n respectively.

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