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A culture of bacteria has an initial population of 220 bacteria and doubles every 8 hours. Using the formula [tex] P_t = P_0 \cdot 2^{\frac{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 11 hours, to the nearest whole number?

Answer :

The population of bacteria in the culture after 11 hours is 581 using the exponential decay formula.

What is meant by population?

The total number of people living in a particular area, such as a city or town, region, country, continent, or the entire world, is typically referred to as the population. Governments frequently conduct censuses to estimate the number of residents living within their jurisdiction. A census is a process for gathering, analyzing, compiling, and releasing statistics regarding a population.

A culture of bacteria has an initial population of 220 bacteria, which doubles every eight hours, according to the information provided.

By applying the formula,

P(t)=P₀.[tex]2^{t/d}[/tex]

P(t) is the population at the end of t hours.

P0 is the starting populace.

d is the doubling time, while t is the time in hours.

After 11 hours, we are asked to determine the bacteria population.

First, we will enter the following values in the doubling life formula as substitutes:

P(t)=220([tex]2^{t/8}[/tex])

Now we will substitute t=11 in our formula to find the population of bacteria after 11 hours as follows:

P(11)=220([tex]2^{17/8}[/tex])

P(11)=220([tex]2^{1.4}[/tex])

P(11)=220(2.639015822)

P(11)=580.5834807≈581

P(11)=581

Consequently, after 11 hours, there will be 581 bacteria.

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