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?

Answer 1

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.