35 40 i The small ants first destroy the large ant colony in year The large ants harvest the fruit in e Textbook and Media 5 Save for Later 10 35 (b) The small ants go to war against the large ants; they c ants. Use your table to determine the first year in which Q Search 15 20 25 30 (c) As long as the large ant population is greater than the small ant population, the large ants harvest fruit th between the two colonies. In which years in your table do the large ants harvest the fruit? 40 V he large ant colony when there are twice pens. hp Attempts: 0 of H myhp
35 40 i The small ants first destroy the large ant colony in year The large ants harvest the fruit in e Textbook and Media 5 Save for Later 10 35 (b) The small ants go to war against the large ants; they c ants. Use your table to determine the first year in which Q Search 15 20 25 30 (c) As long as the large ant population is greater than the small ant population, the large ants harvest fruit th between the two colonies. In which years in your table do the large ants harvest the fruit? 40 V he large ant colony when there are twice pens. hp Attempts: 0 of H myhp
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![**Current Attempt in Progress**
In year \( t \), the population, \( L \), of a colony of large ants is \( L = 8000(1.05)^t \), and the population of a colony of small ants is \( S = 4000(1.1)^t \).
**(a)** Construct a table showing each colony's population in years \( t = 5, 10, 15, 20, 25, 30, 35, 40 \).
Round your answers to the nearest integer.
\[
\begin{array}{|c|c|c|}
\hline
t & L & S \\
\hline
5 & & \\
\hline
10 & & \\
\hline
15 & & \\
\hline
20 & & \\
\hline
25 & & \\
\hline
30 & & \\
\hline
35 & & \\
\hline
40 & & \\
\hline
\end{array}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faeeca323-3b43-4b4c-a978-afa81230e85e%2F8c8d2054-c70b-4275-bb5c-f6622140cb8f%2F6zszmu_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Current Attempt in Progress**
In year \( t \), the population, \( L \), of a colony of large ants is \( L = 8000(1.05)^t \), and the population of a colony of small ants is \( S = 4000(1.1)^t \).
**(a)** Construct a table showing each colony's population in years \( t = 5, 10, 15, 20, 25, 30, 35, 40 \).
Round your answers to the nearest integer.
\[
\begin{array}{|c|c|c|}
\hline
t & L & S \\
\hline
5 & & \\
\hline
10 & & \\
\hline
15 & & \\
\hline
20 & & \\
\hline
25 & & \\
\hline
30 & & \\
\hline
35 & & \\
\hline
40 & & \\
\hline
\end{array}
\]
Transcribed Image Text:The image appears to be from an educational exercise related to ant colony dynamics, possibly in a mathematical or biological context. Below is a transcription suitable for an educational website, incorporating a detailed explanation:
---
**Ant Colony Dynamics Exercise**
**Part (b): Ant Colony Conflict Scenario**
The small ant colony goes to war against the large ant colony. This happens when the population of the small ants reaches twice the size of the large ants. Use your calculations to determine the first year in which this event occurs.
- **Question:** In which year do the small ants first destroy the large ant colony?
- **Answer Options:** A dropdown menu is provided with options: 5, 10, 15, 20, 25, 30, 35, 40.
**Part (c): Fruit Harvesting by Large Ants**
As long as the population of the large ants is greater than that of the small ants, the large ants harvest the fruit that grows between the two colonies. Determine during which years this harvesting takes place based on your table calculations.
- **Question:** In which years do the large ants harvest the fruit?
- **Answer Field:** You are provided a field to enter the years identified from your table.
**Additional Resources:**
For further study, please refer to the available eTextbook and accompanying media for in-depth explanations and examples related to ant population dynamics.
---
This exercise involves the application of population dynamics principles, requiring students to analyze growth patterns and competitive interactions between ant colonies.
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