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 nth hour?

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 2^nd hour = ar² = 30 × 2² = 120

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

⇒ The culture at the end of n^th hour = arⁿ = 30 × 2ⁿ

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