Question

A culture of bacteria has an initial population of 420 bacteria and doubles every 5 hours. Using the formula Pₜ = P₀ ∙ 2ᵗ/ᵈ, 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, what is the population of bacteria in the culture after 9 hours, to the nearest whole number?

Answer 1

The population of the bacteria in the culture after 9 hours is approximately 1514, using the given exponential growth formula and rounding the answer to the nearest whole number.

Step-by-step explanation:

The question is asking how to calculate the population of bacteria after 9 hours, given that the initial population was 420 and the bacteria doubles every 5 hours. We can use the given exponential growth formula Pₜ = P₀ ∙ 2ᵗ/ᵈ to find the answer.

Substituting the values, P₀ = 420 (initial population), t = 9 (time in hours), and d = 5 (doubling time), we get Pₜ = 420 ∙ 2⁽⁹⁄⁵⁾. Using a calculator, we find that 2⁽⁹⁄⁵⁾ ≈ 3.61. Multiplying 420 by this, our answer is Pₜ ≈ 1514.23 which rounds to 1514, to the nearest whole number.

So after 9 hours, the bacteria population is approximately 1514 organisms.

Learn more about Exponential Growth