A Population of Bacteria Is Introduced into a Nutrient Solution $P(t)=\frac{5000}{6+e^{-5 t}}$

question 18

Multiple Choice

A population of bacteria is introduced into a nutrient solution in a dish.The nutrient solution is replenished by the exact same amount each day.At first the bacteria population grows very quickly.Soon, population growth must slow down, as the nutrients become more scarce given the number of bacteria.Eventually the bacteria population stabilizes.A model for the bacteria population growth is given by $P(t) =\frac{5000}{6+e^{-5 t}}$
thousand bacteria.What is $\lim _{t \rightarrow \infty} P(t)$
?

• A)6000
• B)1000
• C)833
• D)5000
• E)None of the above

---

Definitions:

Statistical Information

Data collected and analyzed to represent quantitative aspects of a subject, often used in research and decision-making.

Almanacs

Almanacs are annual publications that include information like weather forecasts, farmers' planting dates, tide tables, and other statistical data and articles.

Government Publications

Documents and materials published by local, state, or national governments to inform the public or document activities.

Business Books

Publications that provide insights, strategies, and advice on a wide range of business-related topics, helping professionals and entrepreneurs succeed.