Question

A culture of bacteria has an initial population of 92000 bacteria and doubles every 7 hours. Using the formula Pₜ = P₀· 2ᵗ/ᵈ , where Pₜ is the population after t hours, Po is the initial population, t is the time in hours and d is the doubling time, what is the population of bacteria in the culture after 5 hours, to the nearest whole number?

Answer 1

The population of bacteria in the culture after 5 hours, given an initial population of 92000 bacteria and a doubling time of 7 hours, is approximately 417,371.

Step-by-step explanation:

The given population growth formula is Pₜ = P₀· 2ᵗ/ᵈ , where Pₜ is the population after t hours, Po is the initial population, t is the time in hours, and d is the doubling time.

Using this formula, we can find the population of bacteria in the culture after 5 hours, given an initial population of 92000 bacteria and a doubling time of 7 hours:

Pₜ = 92000· 2ᵗ/ᵈ

P₅ = 92000· 2⁵/⁷

P₅ = 92000· 32/7

P₅ ≈ 417,371

Therefore, the population of bacteria in the culture after 5 hours is approximately 417,371.