Question

A culture of bacteria has an initial population of 6900 bacteria and doubles every 9 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 11 hours, to the nearest whole number?

Answer 1

To find the bacteria population after 11 hours, we use the exponential growth formula Pt = P0 · 2t/d with the initial population of 6900 and doubling time of 9 hours, yielding the result after calculation and rounding to the nearest whole number.

Step-by-step explanation:

The question pertains to the calculation of bacterial population after a given number of hours using the formula for exponential growth, which is common in biological processes such as bacterial replication. The initial population (P0) is 6900 bacteria, and the population doubles every 9 hours (d = 9). To find the population after 11 hours (t = 11), we use the formula Pt = P0 · 2t/d. Substituting the given values, we have:

Pt = 6900 · 211/9

Using a calculator to perform the exponential calculation, we will get the population of bacteria after 11 hours. Since we want the answer to the nearest whole number, we'll round off the result accordingly.