After how many years will the population be 253? Round to the nearest year.

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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A hunting club stocks a wildlife preserve with 20 elk. The carrying capacity of the preserve is 300 animals and the growth of the herd, allowing for the effect of controlled hunting of the elk, is expected to be modeled by the logistic curve *PICTURE*

 

where t is measured in years. After how many years will the population be 253? Round to the nearest year.

The image shows a mathematical function used to model a particular scenario. The function is given by:

\[ p(t) = \frac{300}{1 + 14e^{-0.157t}} \]

In this expression:

- \( p(t) \) represents the function of time, \( t \).
- The numerator is a constant, 300.
- The denominator consists of 1 plus 14 times the exponential function \( e^{-0.157t} \), where \( e \) is the base of the natural logarithm. 

This type of function is commonly used in modeling population growth, chemical reactions, or similar processes where change occurs over time while considering an asymptotic behavior.
Transcribed Image Text:The image shows a mathematical function used to model a particular scenario. The function is given by: \[ p(t) = \frac{300}{1 + 14e^{-0.157t}} \] In this expression: - \( p(t) \) represents the function of time, \( t \). - The numerator is a constant, 300. - The denominator consists of 1 plus 14 times the exponential function \( e^{-0.157t} \), where \( e \) is the base of the natural logarithm. This type of function is commonly used in modeling population growth, chemical reactions, or similar processes where change occurs over time while considering an asymptotic behavior.
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