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

Given, the number of bacteria was 30 and its doubles every hour.

So, the series is in from of G.P. where First term of the series is 30 and common ratio is 2.

Now, the third term of the G.P. represents the number of bacteria in 2 nd hour.

a 3 =a r 2 =( 30 ) ( 2 ) 2 =120

The number of bacteria at the end of 2 nd hour is 120.

Now, the fifth term of the G.P. represents the number of bacteria in 4 th hour.

a 5 =a r 4 =( 30 ) ( 2 ) 4 =480

The number of bacteria at the end of 4 th hour is 480.

Now, the n th term of the G.P. represent the number of bacteria in n th hour.

a n+1 =a r n =( 30 ) ( 2 ) n

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