High School

A culture of bacteria has an initial population of 13,000 bacteria and doubles every 3 hours. Using the formula [tex] P_t = P_0 \cdot 2^{t/d} [/tex], where [tex] P_t [/tex] is the population after [tex] t [/tex] hours, [tex] P_0 [/tex] is the initial population, [tex] t [/tex] is the time in hours, and [tex] d [/tex] is the doubling time, what is the population of bacteria in the culture after 13 hours, to the nearest whole number?

Answer :

The population of bacteria in the culture after 13 hours is approximately 174,319 bacteria.

What is initial population?

Initial population refers to the starting number of individuals or organisms in a given population at a particular point in time, before any changes or growth occur.

According to question:

In this scenario, the initial population P0 = 13000, the doubling time d = 3, and the time elapsed t = 13. Using the formula Pt = P0 • 2^(t/d), we can calculate the population after 13 hours as follows:

Pt = P0 • 2^(t/d)

Pt = 13000 • 2^(13/3)

Pt ≈ 174,318.68

When this is rounded to the closest whole number, we obtain:

Pt ≈ 174,319

Therefore, the population of bacteria in the culture after 13 hours is approximately 174,319 bacteria.

For example, in a population ecology study of a particular species, the initial population size could be used as a baseline to measure population growth or decline due to factors such as environmental changes or human impact.

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