1. A breeding group of foxes is introduced into a protected area and exhibits logistic population 37.5 0.25 +0.76 growth. After t years the number of foxes is given by: N(t) = Make a graph of N versus t covering the first 20 years. Calculate N(9) and explain in practical terms what your answer means. For what values of t is the graph concave up? For what part of the graph is concave down? JAIL a. b. C.

1. A breeding group of foxes is introduced into a protected area and exhibits logistic population 37.5 0.25 +0.76 growth. After t years the number of foxes is given by: N(t) = Make a graph of N versus t covering the first 20 years. Calculate N(9) and explain in practical terms what your answer means. For what values of t is the graph concave up? For what part of the graph is concave down? JAIL a. b. C.

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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Question

**Exercise 1: Population Dynamics of Foxes**

A breeding group of foxes is introduced into a protected area and exhibits logistic population growth. After $ t $ years, the number of foxes is given by the formula:

\[ N(t) = \frac{37.5}{0.25 + 0.76^t} \]

**Tasks:**

a. **Graphical Representation:**
- Create a graph of $ N $ versus $ t $ covering the first 20 years.

b. **Calculation and Interpretation:**
- Calculate $ N(9) $ and explain in practical terms what your answer represents.

c. **Graph Analysis:**
- Identify the values of $ t $ for which the graph is concave up. Determine the part of the graph that is concave down.

d. **Carrying Capacity:**
- Determine the carrying capacity (the limiting value of $ N $).

**Additional Exercises:**

2. Solve the given problem.

Note: The next steps or content for problem 2 are not visible in the image provided.

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