The number of bacteria in a certain culture doubles every hour. If there were 30 bacteria Class 9

The number of bacteria in a certain culture doubles every hour. If there were 30 bacteria Class 9

Question 1.

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 the 2^nd hour, 4^th hour and n^th hour ? Class 9

Solution:

Initial number of bacteria = a = 30

Since the count doubles every hour

∴ The sequence of number of bacteria after n^th hour is

Explicit rule for the number of bacteria after n^th hours is,

t_n = 30 × 2ⁿ

At the end of 2^nd hour,

t₂ = 30 × 2² = 120 and

At the end of 4^nd hour,

t₄ = 30 × 2⁴ = 480.