The number of bacteria in a certain culture doubles every hour. If there were 30 bacteria present in the culture originally,

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 a₃ = ar² = (30) (2)² = 120

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

a₅ = ar⁴ = (30) (2)⁴ = 480

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

a_{n +1} = arⁿ = (30) 2ⁿ

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

Number of bacterias increasing in each hour is given by 

30 x 2 x 30 x 2² ,30 x 2³ ,30 x 2⁴…….. is in G.P. 

Number of bacteria present at the end of, 

2^nd hour = 30 x 2²  = 120 

4^th hour = 30 x 2⁴  = 30 x 16 = 480 and n^th hour = 30 x 2ⁿ