The doubling time of a type of bacteria is 35 minutes. If every bacterium reproduces, then after 35 minutes a population of 64 bacteria will have grown approximately to what size?
128
The doubling time of a type of bacteria is 35 minutes. If every bacterium reproduces, then after 35 minutes a population of 64 bacteria will have grown approximately to what size?
To calculate the approximate size of the population after a given time, we need to understand the concept of doubling time.
The doubling time is the amount of time it takes for a population to double in size. In this case, the doubling time of the bacteria is given as 35 minutes. This means that every 35 minutes, the population of bacteria will double.
To calculate the approximate size of the population after a given time, we can use the formula:
N = N₀ * (2^(t/d))
Where:
- N is the final population size
- N₀ is the initial population size (in this case, it is given as 64)
- t is the time elapsed (in this case, it is also 35 minutes)
- d is the doubling time (35 minutes in this case)
Substituting the values into the formula:
N = 64 * (2^(35/35))
Simplifying the formula:
N = 64 * (2^1)
Calculating:
N = 64 * 2
N = 128
Therefore, after 35 minutes, a population of 64 bacteria will have grown approximately to a size of 128 bacteria.