There are initially 1000 bacteria in a culture. the number of bacteria doubles each hour. the number of bacteria n present after t hours is . how long will it take the culture to increase to 50,000 bacteria?

There are several information's of immense importance already given in the question. Based on those information's the answer can be easily deduced. 
Initial number of bacteria in the culture = 1000
Number of bacteria after t hours = 1000 (2)^t
Then
1000 (2)^t = 50000
2 ^t = 50
t = 5.6

I hope the procedure is clear enough for you to understand.

The correct answer is a