Answer :
Final answer:
Using the formula pₜ=p₀×2(d/t), an initial population of 13000 bacteria that doubles every 3 hours will be approximately 104,000 bacteria after 13 hours, which corresponds to option C) 104,000.
Explanation:
To calculate the population of bacteria after 13 hours, we will use the given formula pₜ=p₀×2(d/t), where pₜ is the population after t hours, p₀ is the initial population, t is the time in hours, and d is the doubling time in hours. In this case, p₀ = 13000, d = 3, and t = 13 hours.
Firstly, we need to determine the number of doublings that occur within 13 hours, which we do by dividing t by d: t/d = 13/3. Since we cannot have a fraction of a doubling, we round the number of doublings to 4 (since 4.33 doublings is not possible). So, the population after 13 hours is:
pₜ = 13000 x 2(13/3)
Using a calculator, the exact population comes out to 103,680, but we round to the nearest whole number:
pₜ = 103,680
≈ 104,000 bacteria.
Therefore, the population of bacteria in the culture after 13 hours is approximately C) 104,000 bacteria.