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

At present there are 30 bacteria,

--> at the end of second hour, there would be 60 bacteria (30 = 1 hr , 60 = 2 hr)

--> at the end of 4th hour, it would be the product of bacterium in first hour with 4... Since its end of 4th hour.

so at the end of 4th hour there would be = 30*4 = 120 bacteria.

--> bacteria at nth hour;

    using G.P,

a = 30,

r = 2,

n = n+1

An = Ar^n-1

     = (30)(2)^n+1-1

     = 30*2^n

so the bacteria present at nth hour is 30*2^n