High School

A culture of bacteria has an initial population of 230 bacteria and doubles every 9 hours. Using the formula

\[ P_t = P_0 \cdot 2^{t/d} \]

where

\[ P_t \] is the population after \( t \) hours,

\[ P_0 \] 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 13 hours, to the nearest whole number?

Answer :

The population of bacteria in the culture after 13 hours is approximately 876.

How does the formula used to solve this problem relate to exponential growth?

A quantity expands at an increasing rate proportionate to its present size through the process of exponential growth. In this instance, the number of bacteria is expanding exponentially since it doubles every 9 hours. The equation for exponential growth, P(t) = P(0) * e(kt), is used to answer this problem. P(0) is the beginning population, t is the amount of time that has passed, e is a mathematical constant that is roughly equivalent to 2.71828, and k is the growth rate constant.

Given that the equation of the growth is:

[tex]P(t) = P(0) * 2^{(t/d)}[/tex]

d = 9 hours (given)

P(0) = 230 (given)

t = 13 hours (given)

Substituting the values we have:

[tex]P(t) = 230 * 2^{(13/9)}[/tex]

P(t) ≈ 876

Hence, the population of bacteria in the culture after 13 hours is approximately 876.

Learn more about exponential function here:

https://brainly.com/question/11487261

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