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?

Solution:

It is given that the number of bacteria doubles every hour.

Hence, the number of bacteria after every hour will form a G.P with a = 30 and r = 2

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

a = ar²

= 30 x (2)²

= 120

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

a = ar⁴

= 30 x (2)⁴

= 480

The number of bacteria at the end of the n^th hour will be:

a_{n + 1} = arⁿ

= 30 x (2)ⁿ

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NCERT Solutions Class 11 Maths Chapter 9 Exercise 9.3 Question 30

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?

Summary:

There were 30 bacteria present in the culture originally given that the number of bacteria in a certain culture doubles every hour. The answers are 120, 480, and 30 x (2)ⁿ