Question

Proteus vulgaris has a doubling time of roughly 28 minutes. If an initial population of 500 cells is allowed to grow for 6 hours in ideal conditions, what will be the final population? Use three significant figures for your final answer.

Answer 1

Answer: The final population of Proteus vulgaris after 6 hours is $3.71\times 10^{6}cells$

Explanation:

We are given:

Proteus vulgaris divides and doubles every 28 minutes

Total time given = 6 hours = 360 min      (Conversion factor: 1 hr = 60 min)

Number of times Proteus vulgaris doubles in 6 hours = $\frac{360min}{28min}=12.857times$

Calculating the number of bacteria after 6 hours under ideal conditions:

We are given:

Initial population = 500 cells

Number of times it doubles = 12.857 times

Final Proteus vulgaris population = $500\times 2^{12.857}=3709476.8=3.71\times 10^{6}cells$

Hence, the final population of Proteus vulgaris after 6 hours is $3.71\times 10^{6}cells$