Solve.
-A single bacterium divides every 0.5 hour to produce two complete bacteria. If we start with a colony of 6000 bacteria, after t hours there will be
A) 133,084 bacteria
B) 2,129,348 bacteria
C) 8,517,393 bacteria
D) 34,069,570 bacteria

Question

Solve.
-A single bacterium divides every 0.5 hour to produce two complete bacteria. If we start with a colony of 6000 bacteria, after t hours there will be 
A) 133,084 bacteria 
B) 2,129,348 bacteria 
C) 8,517,393 bacteria 
D) 34,069,570 bacteria

Quizplus · Accepted Answer

We can use the formula:

N = N₀×(2^t/Δt)

where 
N₀ = initial number of bacteria = 6000
t = time elapsed in hours
Δt = time for one bacteria to divide = 0.5 hours

Substituting the values, we get:

N = 6000×(2^t/0.5)

Simplifying this expression, we get:

N = 12,000×(2^t)

Now, we need to find the value of N when t = 5.

N = 12,000×(2^5)

N = 12,000×32

N = 384,000

Therefore, the final number of bacteria after 5 hours is 384,000. However, this is not one of the choices given in the question. We need to choose the option that is closest to 384,000.

Option C, 8,517,393, is the closest to 384,000. Therefore, the best choice is C.

Solve. -A Single Bacterium Divides Every 0.5 Hour to Produce Two