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, 4^th hour and n^th hour ?

Answer 1

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

Number of bacteria originally = 30.

Since the bacteria doubles every hour, the numbers form a geometric progression.

First term, \( a = 30 \)
Common ratio, \( r = 2 \)

The number of bacteria present after n hours is given by:

\[ a_n = a r^n \]

At the end of the 2^nd hour:

\[ a_2 = 30 \times 2^2 = 30 \times 4 = 120 \]

At the end of the 4^th hour:

\[ a_4 = 30 \times 2^4 = 30 \times 16 = 480 \]

At the end of the n^th hour:

\[ a_n = 30 \times 2^n \]

Thus, the number of bacteria present at the end of the 2^nd hour is 120, at the end of the 4^th hour is 480, and at the end of the n^th hour is \( 30 \times 2^n \).