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 2nd hour, 4th hour and nth 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.

an +1 = arn = (30) 2n

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